A record 191 members of Parliament's upper house have lined up to speak in what is likely to be the largest second reading debate
in the chamber's history.
No one expects the peers to block the UK's departure from the 27-nation EU, but they could vote at the committee stage to accept amendments to the bill. The legislation would have to go back to the House of Commons if the House of Lords adds amendments, which would delay the bill's passage, endangering Downing Street's March 31 deadline to trigger the Brexit process.
For the first time in living memory, a British Prime Minister was present during a House of Lords debate.
On Monday, Prime Minister Theresa May sat on the steps in front of the royal throne, a position she is entitled to occupy as a member of the Queen's Privy Council
, a group of advisers to the monarchy that includes present or former members of the House of Commons or House of Lords.
The move was widely interpreted as a warning to the upper house not to thwart Brexit plans where the government does not have a clear majority. Many Conservative members of the House of Lords also opposed Brexit.
Britain voted 52% to 48% to leave the EU in a June 24 referendum.
Warnings of 'protracted' conflict
While he voted against leaving the EU, ex-Foreign Secretary William Hague told the chamber Monday that to block the process now "would open up the most protracted, bitter, potentially endless conflict in British society and politics that we have seen since the decades of debate on Irish home rule and possibly even longer than that."
Former UK Supreme Court justice, Lord Browne of Eaton-under-Heywood, an independent, said he supported the bill with the "deepest misgivings."
"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.
'A responsibility ... to the prosperity of our country'
Former EU Trade Commissioner Peter Mandelson, who is vehemently opposed to leaving the bloc, warned against Brexit "at any cost."
"We have a responsibility, not to next year's growth figures, or inflation figures, but to the prosperity of our country for decades to come," he said.
A bill was introduced in the House of Lords on February 8 after the House of Commons approved it unamended, as opposition lawmakers feared upsetting their constituency electorate who had voted for Brexit.
A spokeswoman for the House of Lords told CNN it was "highly unlikely but not impossible" that there would be a vote Tuesday.