Earlier, during his speech, Sir Keir Starmer, the shadow Brexit secretary, said the inclusion of the Northern Ireland amendment in the EU Withdrawal Bill meant the only option was to now "reproduce the customs union and the single market" - effectively making a 'no deal' Brexit impossible.

The Northern Ireland amendment obliges the government to ensure that the Brexit agreement does not disrupt co-operation between the North and the Republic. This means there will not be any physical infrastructure on the Irish border, "including border posts, or checks and controls," Sir Keir says.

He added that the inclusion of the amendment also makes the maximum facilitation or "max fac" option - where new technology would be used to deal with cross-border trade - "unlawful". Max fac is Brexit Secretary David Davis's preferred option for dealing with the Irish border.

You can read more about the government's customs options here.

Tory pro-EU MPs supported the Labour frontbencher's view:

Heidi Allen, Conservative MP for South Cambridgeshire, said: "It's huge, it actually says I think logically we will have to come to a customs union agreement, partnership, love dance, don't care what you call it, that's what we will need to avoid any border to Northern Ireland."

Dominic Grieve also agreed, saying: "Not only will we have to stay in a form of customs arrangement amounting to a union, but we're also going to have to have a high level of regulatory alignment."

And Ken Clarke called the passing of the amendment "the most significant thing that happened yesterday".

What does the government say?

In response to a question from Labour's Chuka Umunna, who asked: "Does he [the solicitor general, Robert Buckland] accept that if we were to leave with no deal and we were trading on WTO rules, that under WTO rules would necessitate a border, therefore leaving with no deal is inconsistent with government policy as he has just stated it?" Mr Buckland replied: "I entirely agree: the government's policy is to achieve a deal because we are mindful of the points that he and others understand."

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Conservative Bob Neill says that he has two tests for Brexit: one is that there is no hard border in Northern Ireland and the second is that it "looks after the economic wellbeing of my constituents and the public services that they depend upon".

"The customs union is not perfect," he says - adding that he will not support the amendments tonight, but, he says, this is because this is not the bill to add these amendments.

"I do say to the government, when we return to the Trade bill...that is the time to have that debate, if a practical outcome is something that looks like a union, call it an arrangement, I don't mind, I want to give the prime minister the flexibility to achieve that."

He finishes:

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Labour's Phil Wilson says that 62.3% of his regions' exports are with the EU, and he points to the President of the CBI's comments today on the car industry- in which Paul Dreschler said sections of the UK car industry "face extinction" unless the UK stays in the Customs Union.

"Everyone knows someone in the north east who does something for Nissan," he says, adding that the EU has been "good" to the north east of England from the investment they have had.

"The economic consequences of leaving the EU remain the same," he says, adding that grievances in the north east have still not been sorted since the vote.

Brexit will turn out to be not the "panacea that people believe it to be," he adds.

He finishes by saying he will be supporting Lords amendment 51 today.

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Conservative MP and former immigration minister Mark Harper says that immigration was "one of the most important issues" in the 2016 EU referendum campaign.

He says it's often "immigrants themselves who want a properly controlled immigration system" because when immigration is properly controlled they have more support.

He says problems arise "when you lose control of a system".

Addressing Remain-minded MPs, who have spent the afternoon suggesting reforms to free movement, he says they are "living in another world".

He says that when David Cameron tried to renegotiate the UK's membership of the EU in the run-up to the referendum vote, other leaders were "not willing to engage seriously" on free movement reform.

He says that "if they had done, I suspect the country would have made a different decision".

As such he says he won't be voting for the EEA amendment today.

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Green Party co-Leader Caroline Lucas says she is "surprised that the government has not simply accepted" the Lords amendment on protecting the environment.

She asks for a new environmental watchdog in the UK to have a real "bark".

"Lords amendment 3 sought to give at least a few teeth to this watchdog," she adds.

The amendment in lieu gives no guarantees on the independence of the environmental watchdog, and makes it more of a "green poodle", she says.

She accuses the government of taking part in a "lazy attempt in standing up for nature".

She pleas with the Labour frontbench "do not give this shambles of a Tory government a free pass to a hard Brexit, it is not too late to reconsider...history will not judge kindly those who put party politics before this most crucial moment, when it is precisely those with the least who most need their politicians to be brave," she finishes.

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Conservative Andrew Percy says that 70% of his constituency voted to leave, adding that he believes that the vote to leave should be respected.

"There are people intent on wrecking and overturning that result," he adds.

He says that there is a "smear" against Leave voters who voted against the political class by branding them as racists and anti-immigrant.

He says that people "want to know that there is a system in place" to control immigration.

"Customs arrangements were not a big part of the referendum campaign," he adds, saying that "we need to come to...a sensible customs arrangement".

MPs are back debating the EU bill after the government avoided a Commons rebellion.

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Conservative Baroness Verma is opening a debate on a report from the European Union Committee called Operation Sophia: A failed mission, external.

Operation Sophia, an initiative undertaken by 25 EU member states, including the UK, was launched in 2015 in the wake of disasters in which hundreds of migrants drowned attempting to reach Europe.

Its aim was to help disrupt organised criminals involved in human smuggling and trafficking networks in the southern central Mediterranean.

She says the problem is that people-smuggling "begins onshore so a naval operation is the wrong tool", but that's "not to say it hasn't been a humanitarian success".

Most of the people arrested by Operation Sophia have been "lower down the food chain", she tells peers, and more needs to be done to take action in source countries.

She says it's a "live issue" as demonstrated by Italy's recent refusal to accept a charity boat of migrants.

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Hywel Williams of Plaid Cymru says "reality is intruding" on the Conservatives and Labour.

He says that like the EU, "Wales needs answers" on the UK's negotiating position and blames Brexiteers for avoiding hard questions.

He says there cannot be two different trade systems in one country, and the arrangements in Belfast will have to be the same as those in the rest of the UK.

He reiterates his party's support for the EEA and customs union.

The Solicitor General, Robert Buckland has said that the government agreement to "further discussions" on the meaningful vote may or may not result in a change.

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Conservative MP Anna Soubry calls Caroline Flint's speech "one of the saddest speeches that I've ever heard" that she "profoundly disagrees" with.

She's "appalled that...a member of the Labour Party has not considered the considerable value that immigrants have brought to our country".

Caroline Flint intervenes to say she "made very clear that I wasn't against all immigration" and she and her constituents want a "fair and managed" system.

Anna Soubry says that "those who complain most about immigration are in areas where there is very little of it...it is fear of the stranger, fear of the unknown".

She says MPs must make the "positive case" for immigration.

Nor is immigration uncontrolled, she says. "How do we control it? We call it the market" because "when there are not jobs they do not come".

She says she'll be supporting the customs union amendments and the EEA amendment because there is "no alternative" to the Customs Union and the single market and that MPs have to "suck it up".

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Labour's Caroline Flint says she is not supporting amendment 51 because the central choice for Parliament is if the UK leaves the EU or not.

The EEA agreement helped three small countries, but this would leave the UK taking rules without being able to make them, she adds.

"It demands a new relationship" with the EU, she says, as there is "no precedent" for a country the size of the UK leaving the EU.

"There has to be an end to freedom of movement," she says, adding that there have been concerns about immigration since 2004.

"My constituents...are not against all migration," she adds.

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Liberal Democrat exiting the EU spokesperson Tom Brake says that there is always an option to "ask the passengers if they'd like to change the direction of the ship".

He says that the government's own red lines "have led them into huge difficulties", on customs, the max facilitation model and customs arrangements.

He says that Labour's amendment is "equally a huge dollop of fudge" - and he asks how Labour can expect a new deal with no "new impediments to trade".

He wishes Labour "good luck with that".

He asks if the UK wants to stay in the customs union or the EEA, then why not just remain in the EU?

"The whole scrutiny process of these amendments brings shame on this House," and he says he hopes that the Lords will be allowed more time for scrutiny.

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Vicky Ford, a Conservative ex-MEP, says "we should not be scared to make amendments" and lends her support to the environmental and Northern Ireland amendments.

She says she accepts today's replacement amendment on the Customs Union and says she "expects the government to ensure frictionless trade".

She speaks against the EEA amendment, which she says unacceptably would turn the UK into a "rule-taker".

Finally, she lends her support to the government's compromise on the meaningful vote, which promises a new amendment in the Lords.

"It was a fudge, but it was an important and meaningful fudge," she concludes.

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Labour's Chuka Umunna says Brexit is much like the hayfever he suffers from: "consistently horrendous, and there's very little that can mitigate the effects".

He says he'll support the Labour Party's amendment calling for "full access to the internal market of the European Union" but will also vote for the amendment calling for membership of the EEA. He says the EEA is "not the perfect model" but should be the "starting point" of any discussion.

Staying in the EEA would involve having free movement with the EU as now, and he says he's "never denied that immigration can pose challenges".

But he says that he believes there are reforms to immigration to "better manage it" which are possible now.

He says that many of the problems people see as down to immigration, like an overstretched NHS and large class sizes will not disappear. In fact, he says, problems in public services are likely to get worse because there will be less money for the government's coffers. He says people said similar things about immigrants of his father's generation from the Commonwealth.

He says that just as curbing Commonwealth immigration in the 1970s did not solve problems in public services, leaving the EU and cutting off European migration will not solve problems now. He says only a Labour government can solve these problems by "funding the NHS, investing in schools and so on".

The party clashed with the Speaker after complaining about a "Brexit power grab" by Westminster.

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John Baron, a Conservative MP and firm Leaver, rejects the idea that Brexiteers are against immigration. "We want a fair system," he says, arguing that this would help low-wage workers.

He says a customs union or EEA membership would "sacrifice" the UK's right to negotiate international trade deals, and would go against the government's manifesto.

He encourages the government to remember that "just because Michel Barnier says it, doesn't make it true".