Conservative rebels are not trying to “collapse the government” but a “meaningful vote” before leaving the EU may help to avoid a crisis moment, the leading pro-European backbencher Dominic Grieve has said.

Ministers are preparing for another Commons showdown over an amendment to give MPs a meaningful vote on whatever the outcome of the government’s Brexit negotiations, after the Lords passed an amendment in a landslide vote on Monday night.

Peers voted in favour of a new amendment, devised by Grieve and tabled by Lord Hailsham, by a significantly bigger margin than the last time the issue was debated.

The wording is based on the deal Grieve believed he had struck with the solicitor general, Robert Buckland, in order to avert a government defeat in the Commons by pro-EU Tories last week.

Rebels say agreed wording was changed at the last minute to give MPs a vote only on “neutral terms”, which would give MPs no power to halt a cliff-edge Brexit.

Grieve was criticised in some newspapers over the weekend when he suggested he could “collapse the government” and said he woke up in a cold sweat thinking about it.

The former attorney general said: “One of the reasons I’ve supported [this amendment] is precisely to avoid a situation where the government would immediately collapse,” he said. “And I’ve been misreported on that, it was suggested I want to collapse the government, I don’t.”

Grieve said the new amendment was “a mechanism by which the House of Commons could express a view, without moving to a motion of no confidence, which could collapse the government.

“All of us must hope this doesn’t happen. But there is a risk it will happen, and if we have no deal at the very end it is a serious crisis.”

Several MPs have suggested Grieve’s amendment is unnecessary. The Conservative MP Tom Tugendhat said MPs would be “looking for a new government” if the current one failed to deliver a Brexit deal that could pass the Commons.

Grieve said he did not want to leave such a situation to chance. “If we get to a situation where we are three weeks away from no deal … the idea that it’s a good moment to get a new prime minister, have a general election … it doesn’t seem to me a good moment, if it can be avoided,” he said.

The MP said he hoped a compromise deal could be agreed with the government before the vote on the amendment on Wednesday, but it was “complete nonsense” to suggest the government could fall if Theresa May lost the vote.

Rebel Tories have insisted the prime minister had personally promised them that she would listen to their concerns about MPs having a meaningful say in the event of no deal with the EU.

Grieve said he hoped trust could be restored: “We didn’t get what we had hoped for. I am conscious the prime minister is in great difficulty. I would be very happy if we could resolve this in a way that that trust, which I have always tried to place in the prime minister, is honoured.”

Under the new amendment passed by the Lords, ministers must update parliament by 21 January if there is no prospect of a deal with the EU and then have two weeks to return to the Commons with a statement on how the government plans to proceed. MPs would then be given a vote on whether to approve the action in a statement.

The meaningful vote is the only unresolved issue after peers agreed not to pursue further challenges on other key matters such as membership of the customs union. At the report stage of the bill, peers inflicted 15 defeats on the government.