However, the 252 Tory peers could be outnumbered if Labour and Liberal Democrats peers with 202 an 102 peers, respectively banded together to add amendments to the bill.
Britain's upper house is getting ready to put the government's Brexit bill under scrutiny. Earlier this month, the House of Commons, passed the legislation without amendment.
The message, although silent, was clear: the directly elected House of Commons overwhelmingly passed the draft legislation to trigger Brexit talks and the unelected Lords should follow suit.
The Lords will continue to debate the Brexit Bill today.
Peers are expected to press ministers to guarantee the residence rights of European Union nationals living in Britain and ensure Parliament can reject any possible deal.
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Nearly 200 peers could speak in the debate on the second reading of the European Union (Notification of Withdrawal) Bill this week, before specific amendments to the legislation are considered next week.
In an unusual but not unprecedented move for a prime minister, May made her presence felt on Monday as she also attended the debate at the House of Lords, sitting at the steps to the monarch's throne. The government is still expecting to stick to its timetable of triggering Brexit by the end of March.
"Whatever damage we judge Brexit may do to the national interest, it is still less than the damage which I believe would inevitably be done to the public's trust in the political process if we were now to thwart the majority vote", he said.
"Properly there will be debate and scrutiny in the House of Lords, but I don't want to see anybody holding up what the British people want, what the people of Stoke-on-Trent voted for past year, which is for us to deliver Brexit, to leave the European Union".
He has said it is his "mission" to persuade voters to "rise up" and change their minds on Brexit.
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The House of Lords is more diverse than the Commons, and if its members vote to change the bill, it will kick off a parliamentary ping pong, whereby the legislation must be sent back to the lower house to be reconsidered, before returning to the upper house again.
"It's time the Lords came clear about their European Union money and recognise the decision of the people by backing the Article 50 Bill unamended".
The Conservative led government faced a lot less opposition in the Commons than predicted by some commentators, even from "Remain" Conservatives, and PM Theresa May continues steadfastly towards the United Kingdom exit from the European Union. "As we have seen with the Dubs amendment, we can't always rely just on what the government says".
The ex-business secretary repeated former Labour prime minister Tony Blair's claim that Theresa May is chasing "Brexit at any cost".
But May's spokesman said on Monday: "We've been absolutely clear that Article 50 will not be revoked after notification".
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