Prime Minister Boris Johnson will address his new intake of Conservative MPs later as they arrive in Westminster to take their seats in Parliament.
Many of the 109 new MPs won in areas traditionally held by Labour in Thursday’s election, which saw the Conservatives gain an 80-seat majority.
Their first job will be to vote on the Withdrawal Agreement Bill that the PM intends to bring back before Christmas.
Mr Johnson is also expected to carry out a mini cabinet reshuffle.
He needs to fill posts made vacant by those who stood down ahead of the general election, including the culture and welsh secretary posts.
The Queen will formally open Parliament on Thursday when she sets out the government’s legislative programme.
It is thought the Withdrawal Agreement Bill (WAB) on leaving the EU could be put before MPs as early as Friday.
Ahead of the private speech, a Number 10 source said: “The PM has been very clear that we have a responsibility to deliver a better future for our country and that we must repay the public’s trust by getting Brexit done.
“That’s why the first piece of legislation new MPs will vote on will be the Withdrawal Agreement Bill.”
With the large majority, the bill is expected to pass through Parliament in time to meet Boris Johnson’s promise for the UK to leave the EU on 31 January.
Mr Johnson then has to negotiate a new trade agreement with the EU and have it ratified before the end of the post-Brexit transition period that ends on 31 December 2020. He has repeatedly said that the transition period will not be extended.
The Queen’s speech is also expected to include legislation linked to pledges made during the election campaign – most notably a guarantee on NHS funding.
Moves to get the Northern Ireland goverment at Stormont up and running again are also expected, with talks resuming before Christmas.
Meanwhile, the fallout from Labour’s defeat continues.
Labour’s general secretary says party officials are likely to meet early in the new year to agree the timetable for replacing Jeremy Corbyn as leader.
Mr Corbyn wants the process to begin “swiftly”, Jennie Formby said, so his successor can be in place by the end of March.
She has written to members of Labour’s National Executive Committee (NEC) recommending a provisional date of 6 January for the meeting, with the process beginning the following day.
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Both Jeremy Corbyn and John McDonnell said on Sunday that they took the blame for Labour’s “catastrophic” defeat in Thursday’s election.
Mr Corbyn said he was “sorry that we came up short”, while Mr McDonnell told the BBC he “owns this disaster”.
The race for their replacements has already begun, with Wigan MP Lisa Nandy saying for the first time she was “seriously thinking about” running.
Other possible contenders are shadow Brexit secretary Sir Keir Starmer, shadow business secretary Rebecca Long-Bailey, shadow education secretary Angela Rayner, Jess Phillips, who is an outspoken critic of Jeremy Corbyn, and shadow foreign secretary Emily Thornberry.
A new intake of SNP MPs will also be taking their seats on Tuesday. The party increased its share from 47 to 59 in Thursday’s election.
Leader Nicola Sturgeon has insisted this gives her a mandate for a second referendum on Scottish independence – something the prime minster has told her he remains opposed to.
She said the Conservatives, who lost seven of their 13 seats in Scotland, had been “defeated comprehensively” and that the new MPs would continue to press for independence.
What will happen this week?
Proceedings begin when MPs gather for their first duty: to elect the Speaker, Sir Lindsay Hoyle, who replaced John Bercow in November. Technically, MPs can hold a vote on this motion but this has never happened in practice.
Later in the day, the Speaker will begin the process of swearing in MPs, who are required to take an oath of allegiance to the Crown, or, if they object to this, a solemn affirmation. Those who speak or vote without having done so are deprived of their seat “as if they were dead” under the Parliamentary Oaths Act of 1866.
Two to three days are usually set aside for this process.
The state opening of Parliament. The Queen’s Speech is the centrepiece of this, when she will read a speech written by ministers setting out the government’s programme of legislation for the parliamentary session. A couple of hours after the speech is delivered, MPs will begin debating its contents – a process which usually takes days.
Depending on how rapidly Boris Johnson wants to move, the debate on the Queen’s Speech could continue into Friday.
This may be interrupted for a second reading debate on the Withdrawal Agreement Bill.
MPs in the previous Parliament backed Boris Johnson’s bill at its first stage but rejected his plan to fast-track the legislation through Parliament in three days in order to leave the EU by the then 31 October Brexit deadline.
After the debate on the Queen’s Speech is concluded, MPs will vote on whether to approve it. Not since 1924 has a government’s Queen Speech been defeated.
Read more from the BBC’s parliamentary correspondent, Mark D’Arcy
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