A briefing from the House of Commons Library suggested that only seven bills were passed using the Act of Parliament. The last was the Hunting Act of 2004, which banned fox hunting.
The move would only be necessary if the Lords repudiated rather than amend the small boat law.
Liberal Democrat colleagues attempted such a move earlier this year, but failed to gain enough support. There is still time for another attempt.
During a Lords debate on Monday, colleagues threatened to delay the illegal migration bill unless the Home Office publishes its impact assessment of the measures.
Labour’s Lord Hunt of Kings Heath was met with encouragement when he said the bill should not go to the next stage without the assessment being available.
Lord Murray of Blidworth, a Home Secretary, said it would be published “in due course”.
Meanwhile, Suella Braverman, the interior minister, has been warned of a new wave of Albanian migrants crossing the Channel this summer, despite the crackdown on small boats.
She has been given an internal survey, commissioned by the British Embassy in Tirana, which shows that half of young Albanians want to cross the Channel to Britain this summer.
The poll, based on 1,800 households in Kukes, the main migrant area in northern Albania, found that half of young men aged 17 to 22 wanted to leave their homeland and come to Britain, despite the risks of crossing of the Channel.
On Monday, Ms Braverman said new requirements for asylum seekers to share rooms, first revealed by The Telegraph, would save £250 million a year and reduce the need to search a further 90 hotels.
The Home Office currently spends £6 million a day housing nearly 50,000 migrants in 395 hotels.
However, Lee Anderson, Deputy Chairman of the Conservative Party, warned that “sharing rooms and ships, and relying on the French is not the solution”.
He said: “The answer is … to get the flights to Rwanda out as soon as possible.”
The Court of Appeal will rule within a few days on the legality of the Rwandan expulsion plan. Ms Braverman said the Rwanda plan and new illegal migration law would have a further deterrent effect.
“To stop the boats, we have to move on,” she said.
