House of Commons
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Treasury Committee Chair, the Conservative Nicky Morgan thanks the government for the "early Christmas present" it has given to EU citizens regarding their rights.

She says that the agreement is testament to the power of continuing dialogue with the EU.

Mrs May says she hopes people will look "seriously and carefully" at the negotiated agreement for EU citizens.

She says the negotiation takes hard work and determination.

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Labour's Pat McFadden asks the PM to confirm that if voters do not like the eventual deal "they have every right to change their minds".

Theresa May calls that a "misinterpretation" of comments made by Michael Gove and reiterates there will be no second referendum.

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Anna Soubry, a high-profile Remain supporter, congratulates the PM on "a major step forward" in negotiations and asks when more will be known about the new trade relationship.

Theresa May says legally a new trade deal can't be signed until we've left and it has been approved by national parliaments.

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Lib Dem Leader Sir Vince Cable, suggests that Mrs May might like to "suspend tribal politics" and invite the Leader of the Opposition Jeremy Corbyn to attend talks and negotiations.

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Conservative Tom Tugendhat welcomes the latest developments and asks the prime minister to confirm "we are leaving the EU, not leaving Europe" for the benefit of "European friends".

Theresa May tells him that is the case, and the UK still has work to do in Europe.

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Hilary Benn, Chair of the Exiting the EU Committee, is questioning Mrs May on technical points.

He asks her to confirm if the UK will fall back to regulatory alignment if no agreement is reached.

Mrs May says the UK government believes that agreements will be reached with a negotiated settlement. She says the UK will look at full regulatory alignment as a third last resort.

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The SNP's Westminster leader Ian Blackford says that last week the Prime Minister had the "humiliation" of going back on an agreement because of the DUP. He asks if Arlene Foster is running the UK, or if it is "the Right Honourable Member for Maidenhead".

He asks why other parts of the UK now won't be allowed to remain in the single market.

Mrs May response is that Northern Ireland is the only part of the UK which has a land border with an EU country.

She says that the UK will be leaving the single market and the customs union. She says this is in response to the 2016 vote to leave the European Union.

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Peers vote 172 to 139 to approve a government amendment which sets out requirements for the protection of personal data after Brexit.

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Father of the House Kenneth Clarke asks Mrs May if the UK has now settled the rights of EU citizens in the UK. He says that open borders require regulatory alignment with other countries.

Mrs May says the most detailed area of work so far is on EU citizens' rights.

She says the withdrawal agreement, in its final text, will be brought to the House of Commons

In any trade agreement some alignment is necessary, she says, and in this case, the UK has mostly the same rules as the EU currently has.

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Peers are currently voting on a government amendment which sets out requirements for the protection of personal data after Brexit.

Digital, Culture, Media and Sport Minister Lord Ashton had asked peers to accept his amendment, but Labour spokesman Lord Stevenson of Balmacara said it was better to start with a "blank sheet" and peers forced a vote.

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Responding to Mr Corbyn, Mrs May says that the Labour Party has "had 12 different Brexit plans".

She says the offer of paying around £35bn is subject to agreeing the current partnership offer.

She says continued payment for membership of certain agencies will be decided in phase two of the talks.

Responding to Mr Corbyn's question on what "CETA Plus Plus Plus" means - as mooted by the Brexit Secretary David Davis on Andrew Marr's Sunday morning show, she says the UK is trying to get a bespoke deal.

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Jeremy Corbyn finishes his speech, saying that he hopes the next phase of negotiations won't be "punctuated by posturing, delays and disarray".

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Labour leader Jeremy Corbyn responds to the PM's statement, saying she "scraped through" phase one of negotiations.

Many aspects of the proposed agreement are "still not clear", he continues, and the "shambolic" nature of talks leads him to question whether the government is capable of securing a deal.

He asks for confirmation that the European Court of Justice will oversee citizens' rights for the next eight years and continue to play a role indefinitely, and how this squares with her "red line" that ECJ jurisdiction will end.

He presses for details of how plans for regulatory alignment will work.

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Mrs May says the agreement she has reached will continue the Belfast agreement. The government is, meanwhile, continuing to work on the reinstatement of the Northern Ireland government.

The implementation period talks will now begin and should start as soon as possible, she says, in line with the recommendation of President of the European Council, Donald Tusk.

She says "some doubted we would reach this stage" but adds "nothing is agreed until everything is agreed," prompting laughter from the Labour benches.

There is "a new sense of optimism" in the talks, she adds.

She expects to be able to confirm the agreements that have been reached at the EU Council summit next week.

She adds that we will leave the EU, but will do so in a smooth and orderly way.

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Theresa May is now giving a statement on the agreement to move Brexit talks on to the next phase reached on Friday.

The agreement covers citizens' rights, the financial settlement and the border with the Republic of Ireland.

A clause inserted in Friday's agreement at the insistence of the Republic of Ireland government says the UK would have full "regulatory alignment" with the EU in some areas if it leaves the EU without a deal.

Ms May says that Mr Juncker is now recommending that talks proceed to the next phase of negotiations, which focus on the future relationship between the UK and the EU.

She says that the settlement brings an agreement between the UK and the EU on the 3m EU citizens in the UK and the 1m UK nationals in the EU. The UK will leave the jurisdiction of the European Court of Justice for EU citizens, she says, but pay attention to ECJ rulings.

She adds that the UK will continue to pay into the EU budget under EU rules for the current budget period.

Mrs May says that the deal will represent savings for the UK, which will be money the UK can use for homes, schools and the NHS.

Turning to the Irish border, she says it is important that no new barriers are put in place, and that there will be no new borders within the United Kingdom, the whole of the UK will leave the customs union.

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The SNP's Joanna Cherry is asking a question on EU citizens working in British universities.

She says that in her constituency, one university has made staff redundant. Citing the UK government's Brexit stance as an "approximate cause" she says that at another university potential staff from EU countries are turning down job offers.

Universities Minister Jo Johnson says that "uncertainty is completely unnecessary," because the UK government has given assurances of continued input into programmes such as Horizon 2020, external.

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Peers are now taking part in report-stage debate on the Data Protection Bill, which provides a data protection framework for when the UK leaves the EU.

Digital, Culture, Media and Sport Minister Lord Ashton of Hyde introduces a government amendment which sets out requirements for the protection of personal data, including:

• requiring personal data to be processed lawfully, on the basis of the data subject’s consent
• conferring rights on the data subject to obtain information about the processing of personal data
• giving the Information Commissioner powers to monitor and enforce those provisions.

House of Commons
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Education Minister Anne Milton responds to a question by Labour's Mike Amesbury on apprenticeships, saying that the government is "determined to reach 3 million apprenticeship starts in England by 2020".

She says that there have been 1.1m new apprenticeship starts since 2015. Quality is important, she says, adding there have been 24,600 starts on "employer-designed" apprenticeships.

Mr Amesbury says that the average monthly start for apprenticeships is 17% lower than it needs to be for the government to hit its 2020 target.

He adds that local business leaders are better equipped to deal with apprenticeships "than the Conservative government."

Ms Milton says it is only because of the reforms the government has made that employers are "at the heart" of new reforms.

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Shadow work and pensions spokesperson Baroness Sherlock asks why kinship carers who subsequently have their own child are not exempt from the two-child limit on benefits.

She says that the current rules mean kinship carers who act as guardians for at least two children are refused child tax credits and maternity grants when they decide to have a child of their own.

Work and Pensions Minister Baroness Buscombe says that the government recognises the "immense value" of the contributions made by kinship carers and the policy is kept under review.

Conservative Lord Mackay of Clashfern says he hopes the government will reconsider.

Baroness Buscombe insists the two-child policy helps to "ensure fairness" and meets human rights obligations.

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Liberal Democrat Wera Hobhouse asks a question on home schooling, and whether or not the Education Department has made assessments on the necessary skills for home education.

Education Minister Robert Goodwill says there are some good examples of excellent home schooling from qualified teachers, but he adds it is important that home education is not used as an alternative to exclusion, or "lack of provision of correct special educational needs".

"We are very much on that case," he adds.