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Meanwhile in the Commons, debate is continuing over which of the various alternatives to the PM's Brexit deal they should back in the votes due this evening.

Labour's Phil Wilson, one of the MPs behind the motion for a confirmatory vote on any Brexit deal, says "we now know what Brexit will look like".

He says Brexit was a "viewpoint" and a "concept" which "falls apart in the different schools of thought".

A confirmatory referendum would give the public the right to decide how the final deal compares with the promises made during the 2016 referendum, he says.

Chief Secretary to the Treasury, Liz Truss, calls Mrs May a "patriot".

Welsh AM Adam Price, who leads Plaid Cymru, said Mrs May's actions "would make even Neville Chamberlain blush", referring to the former wartime UK prime minister.

Tory MP Mims Davies tweets - with wording very similar to that of the government's Scotland secretary.

Meanwhile, SNP MP Peter Grant compares Mrs May's statement to that of last week, when she publicly blamed MPs for the Brexit delay.

And the Green Party's Caroline Lucas calls it "frankly obscene".

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In the Commons, Conservative MP Kevin Hollinrake urges his colleagues to back the PM's Brexit deal, rather than any of the eight alternative options that will be voted on later.

The negotiating red lines set out by the government reflect "promises that were made prior to the referendum", he says.

The PM's deal, he says, "does meet the promises that were made". "There is not a simgle motion in this order paper that lives up to those promises", he adds.

The agreement is a "Goldilocks deal - not too hard, not too soft", he says.

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BBC political correspondent Vicki Young says Theresa May's problem is that she doesn't have a majority, and needs the Democratic Unionists' support for her deal to go through.

"The DUP are still central to this and we haven't heard from them yet," she adds.

She says there is movement from Brexiteers such as Jacob Rees-Mogg and possibly Boris Johnson.

"You may see some of them putting aside their negatives about her deal if she is promising to go."

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Parliament

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In spite of all the excitement outside the chamber, the Brexit debate is still going on.

It is now the turn of the Independent Group's Chuka Umunna, who says that after the referendum MPs had "a duty to square the promises made during the referendum with what is deliverable".

However, he says it is "impossible to deliver on the mythical, fantastical promises delivered back then".

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Former Health Minister Steve Brine says Conservative MPs are a close group of people and "there's a lot that unites us, and a lot of respect for the prime minister".

Mr Brine, who quit the government earlier this week, says the prime minister was honest in her address and spoke from the heart, adding that "as ever with Theresa May - she was 'country first'".

He said she had emphasised the fact she did not want Jeremy Corbyn to become prime minister or for Brexit to fail. On whether it will be enough to get her deal through, Mr Brine says "I feel it will be very close".

Iain Watson
Political correspondent

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Conservative Brexiteer Jacob Rees-Mogg now says that if the DUP abstains, he will back the prime minister's deal.

Talks between the government and their Northern Irish partners are continuing as we speak.

The DUP has previously said they are not minded to support the agreement but observers have pointed out that if they abstain, this could pave the way for it getting through.

Meanwhile, Mr Rees-Mogg would not comment on his leadership ambitions.

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Former cabinet minister Nicky Morgan urges MPs to reflect on the PM's announcement and focus on how they can get the Speaker's approval to hold another meaningful vote on the Brexit deal.

She says there were some colleagues who simply weren't going to vote for the agreement unless Theresa May moved on and they now need to think carefully about how they will vote if they get another opportunity.

"It is a fluid situation," she says, noting that this afternoon's developments mean the Speaker "might, just might, allow it to come back".

On indicative votes, Ms Morgan says she hopes the nation will see that MPs are "trying to move forwards", but adds, "I'm not sure if we're going to get a result tonight, it might have to happen again on Monday."

The Scottish Secretary David Mundell is the first cabinet minister to publicly react to the PM's announcement about her future.

Conservative MP Simon Hart, who was in the 1922 Committee meeting where Mrs May made her announcement, said the mood in the room was "respectful" as she set out her plan.

The prime minister, he says, did not give a specific date for her departure while signalling she would not lead the next phase of Brexit negotiations.

"She was passionate about getting the deal through, passionate about keeping the party together and passionate about keeping the government as the government, passionate about keeping Jeremy Corbyn out of Number 10."

He joked that "neither the Chief Whip nor the PM were crying".

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Responding to Mrs May's comments to MPs that she will step down if her Brexit deal is passed, Labour's Dame Margaret Beckett says: "If I were them, I'd want it in blood.

"I've lost track of how many times she's promised them she wouldn't lead them into the next election and then suddenly it's turned out she might after it all."

Asked if she think its will change the dynamics of Wednesday's debate, Dame Margaret says "it's possible, it certainly might change the dynamics of later negotiations".

Downing Street has now officially confirmed what the prime minister told MPs just now. It is pretty striking stuff.

“This has been a testing time for our country and our party," she said.

"We’re nearly there. We’re almost ready to start a new chapter and build that brighter future. "But before we can do that, we have to finish the job in hand.

“I have heard very clearly the mood of the parliamentary party. I know there is a desire for a new approach – and new leadership – in the second phase of the Brexit negotiations – and I won’t stand in the way of that."

“I know some people are worried that if you vote for the Withdrawal Agreement, I will take that as a mandate to rush on into phase two without the debate we need to have. I won’t – I hear what you are saying.

“But we need to get the deal through and deliver Brexit."

Labour MP Jo Stevens called it the "ultimate bribe" to her party.

Anna Soubry - the former Conservative MP who quit the party in February to join the Independent Group - calls it "shameful".

Meanwhile, Labour's Liz Kendall tweets: