The government could promise to make more time for the current bill to be debated this session or, if a backbench MP re-introduces it to Parliament, in the next session.
It has already ruled out re-introducing the legislation as a government bill with Lord Kennedy, the chief whip in the Lords, saying: “I have enough problems getting the government’s programme through at the moment, let alone trying to deal with this bill.
“So I promise you it is not going to come back as a government bill.”
Speaking to the BBC, Leadbeater said: “We now have a piece of legislation which has been voted through by members of Parliament in the Commons.
“I think the government has got a duty to respect that and from a democratic perspective to support getting the bill through.
“The government have been brilliant and have been very neutral because they are very respectful of different views there are in the cabinet and across Parliament.
“But I also think they have a duty to respect the will of the democratically-elected members of Parliament who voted for it.”
A senior Labour MP who asked not to be named warned the prime minister against intervening.
“It would provoke a massive split amongst Labour MPs and the prime minister is not strong enough to bear that,” they said.
Leadbeater has said the majority of peers back her proposals but that a small group of opponents were trying to talk the bill out, also known as filibustering.
Nikki Da Costa – former No 10 adviser and an opponent of the legislation – said peers were not trying to block progress but rather were “doing their best to patch the holes” in “an unsafe, deficient bill”.
Lord Falconer, who along with Leadbeater is shepherding the bill through Parliament, has said the legislation has “absolutely no hope” of becoming law without a “fundamental change” in the House of Lords’ approach.