The House of Lords is debating the European Union (Withdrawal) Bill, which aims to transfer European law into UK law.
Almost 190 peers are listed to speak over the two days of second reading, where the principle of the Bill will be considered.
Debate on the Bill on Tuesday is expected to end after the 94th speaker, Conservative Baroness Morris of Bolton, before resuming on Wednesday.
The upper chamber's red benches were packed as debate started.
Lords Leader Baroness Evans of Bowes Park said it was an honour to open the debate on such an important Bill.
Some suggest that this House will ignore the referendum, or attempt to use the Bill to frustrate the Brexit process. I don't share those concerns.
"This Bill ensures we have a functioning statute book on the day we leave," she told peers.
"It is about providing certainty and continuity for people and businesses. It is about ensuring people's rights are upheld, and legal protections are maintained. It is vital to a smooth and orderly exit from the EU. My Lords, this Bill is not about revisiting the arguments of the referendum.
"Not for the first time, there has been much speculation about what might be expected from Your Lordships' House, as we consider this Bill. Some suggest that this House will ignore the referendum, or attempt to use the Bill to frustrate the Brexit process.
"I don't share those concerns. I am keenly aware of the collective sense of responsibility felt across this House to our important constitutional role and I am confident noble Lords will take a constructive approach to our deliberations."
Labour former transport secretary Lord Adonis proposed a rare motion of regret that the Bill did not provide for a second referendum on the terms of the final Brexit deal.
The final say should rest with the people once they see the terms proposed by the government
Pointing out there were more peers due to speak than in any other debate in the chamber's 800-year history, he said: "It is symbolic and it is because of the magnitude of the issue at stake that I move this motion.
"Just the first say on Brexit was given to the people, so the final say should rest with the people once they see the terms proposed by the government."
Lord Adonis added: "The Prime Minister promises a deep and special partnership with the European Union, when actually we are leaving the union and undermining our deep and special partnership.
"We are told that frictionless trade will arise, amazingly, from the setting up of thousands of trade barriers where they currently don't exist.
"And on the future of Ireland, where Parliament ought to tread with especial care given the tragedies of recent decades, the Government says it intends continued regulatory alignment when its stated policy elsewhere is to discontinue alignment and promote regulatory dealignment.
"The House needs to reconcile rhetoric and reality in all these areas."