Cabinet ministers involved in cross-party talks on how to break the Brexit deadlock have given the first indication that they are prepared to examine plans for a potential second referendum on the UK’s departure from the EU, according to the Liberal Democrat leader, Sir Vince Cable.

The offer to examine a possible timetable for a second vote drawn up by the Lib Dems was made during discussions between senior Liberal Democrats and two cabinet ministers involved in the talks, Michael Gove and David Lidington, in the Cabinet Office on Thursday morning.

While Theresa May’s government remains strongly opposed to the idea of returning the issue of Brexit to the electorate, the revelation by Cable shows that ministers are determined to look at a wide range of ideas being put forward by opposition parties.

The government insists that any referendum that could reverse the 2016 decision to leave the EU would be a betrayal of the will of the people. It has also suggested that a second vote would take up to a year to prepare and conduct. But the Liberal Democrats have produced draft legislation which they say would allow one to be held far sooner: before the next European elections in May.

Cable spoke in the Commons to the prime minister on Wednesday evening, after Labour’s no-confidence motion was defeated and soon after May had said she was ready to open talks on a way forward with opposition MPs, including party leaders. Cable stressed in those talks with May, which were described as “polite and cordial”, that his party’s central demand was for a second referendum.

While May reiterated her opposition to the idea to Cable, senior Lib Dems then repeated the demand at the subsequent meeting with Gove and Lidington on Thursday. The Lib Dems say Gove asked at the second meeting to see the detailed plans, suggesting an active interest.

On Saturday night Cable released to the Observer the text of a letter he has sent to Lidington following the two rounds of discussions. It states: “Further to your meeting with my deputy Jo Swinson, chief whip Alistair Carmichael and Brexit spokesperson Tom Brake, I write – as requested – with further details as to how we consider a referendum could be brought about in May.

“As you will know, we have published on a cross-party basis two bills. The first is a two-clause bill which could be enacted within a week, to enable the Electoral Commission to begin consultation on a referendum question. The second, a substantive referendum bill. Dominic Grieve tabled these in presentation bills in parliament last week.

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“With sufficient political will, a referendum bill could be passed in very short order – perhaps within days. However, we estimate that even without complete consensus across the house, legislation could be passed in six weeks and a referendum could be brought about within 16 weeks. This would enable a ten-week total campaign period (to include designation of campaigns). Proceeding with a people’s vote on this basis is now the only remaining lifeline for the negotiated deal between the UK and the EU27, since no parliamentary majority can be assembled for it without a referendum.”

Cable told the Observer: “Where there is a will, there is a way. If the government moves quickly, as we believe it should, it will be possible to conclude the Brexit story one way or another before the scheduled European parliamentary elections. While Liberal Democrats firmly reject her deal, we have no doubt the prime minister would campaign vigorously for public approval of it. We have long believed giving the public the final say on this deal is the only way forward. This timetable paves the way.”

Lord Tyler, the architect of the Lib Dem timetable, said it was wrong to suggest a referendum would take a year. While it could not take place before the scheduled exit date of 29 March, it could be conducted in a far shorter timeframe than 12 months, although this would involve delaying Brexit.

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Tyler said: “A referendum can be brought about quickly when parliament determines to make it happen. The process for the 1997 devolution referendums took place in 17 weeks from the bill hitting parliament to people casting their ballots.”

Government sources said that any willingness to examine the plans of opposition parties did not indicate a preparedness to adopt them. Downing Street again ruled out Theresa May ever backing a second referendum.