Mrs May sat at the foot of the throne used by the Queen when she addresses parliament and heard the opening remarks in debate on the European Union (Notification of Withdrawal) Bill.
Speaking earlier in Stoke, where a by-election will be held on Thursday, Mrs May warned Peers not to delay the legislation.
Noting that the bill passed the Commons without any amendments, the Prime Minister said: “I hope that the House of Lords will pay attention to that.
“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... which is for us to deliver Brexit, to leave the European Union.”
Opening the debate, Lords leader Baroness Evans of Bowes Park also warned peers against any stalling tactics, telling them the government had a “strong mandate” to trigger Article 50 and start the two-year process of negotiating the UK’s exit from the EU.
Labour and Lib Dem lords have pledged to seek amendments to the bill to secure a guarantee for EU citizens living in the UK, and give MPs the chance to reject the UK’s final Brexit terms and vote to send Mrs May back to the negotiating table with Brussels.
“This Bill is not the place to try and shape the terms of our exit, restrict the Government’s hand before in enters into complex negotiations or attempt to re-run the referendum,” Baroness Evans warned.
Labour’s leader in the Lords, Baroness Smith of Basildon, said her party “will not block, wreck or sabotage” the legislation, but added: “I have also said neither shall we provide the Government with a blank cheque.”
Baroness Smith said: “It would be irresponsible to merrily wave the Government off to negotiate our future without parliamentary engagement or accountability and merely ask them to return two years later with a deal.”
Lord Hope of Craighead, the former head of the Scottish judiciary and the leader of the independent crossbench peers, said the Bill “leaves many questions unanswered on which we will wish to hold the Government to account,” but added that he would not seek “to tie the Government’s hands” before it started the formal Brexit process.
There was criticism from Brexit-supporting peers, with William Hague turning his fire on former Prime Minister Tony Blair. “Attempts to re-fight that referendum, which have begun a little in the last few days, are a great error,” Lord Hague said. “Asking people to ‘rise up’ to fight Brexit, in the words a few days ago of Mr Blair, are a great mistake.”
Lord Forsyth, the former Scottish Secretary, called the Lib Dems “beached whales swimming against the democratic tide” for seeking a second referendum on the terms of Brexit.
If peers force amendments, the bill will return to the Commons for further debate. The government has said it will keep to its March 31 deadline for triggering Brexit.