Britain could be edging closer to a December election after the Liberal Democrats abandoned their focus on a second referendum to push for an election plan that could circumvent Labour’s opposition, bringing tentative support from Downing Street.

A formal proposal by the Lib Dems and Scottish National party to seek an election on 9 December by amending the Fixed-term Parliaments Act (FTPA) was dismissed by the Tory party chair, James Cleverly, as a “gimmick”.

However, No 10 sources subsequently said that if MPs rejected a government motion to seek an election under the FTPA for a third time on Monday, Boris Johnson could eventually be forced to explore a similar route to the Lib Dem plan.

FTPA election motions require at least two-thirds of MPs to support them, giving Labour an effective veto on the process. In contrast, calling an election via an amendment to the FTPA, or a separate one-line act, would only need a straightforward majority in the Commons.

The Downing Street source said: “If Labour oppose being held to account by the people yet again then we will look at all options to get Brexit done, including ideas similar to that proposed by other opposition parties.”

The route is nonetheless by no means clear. The Lib Dem-led plan, set out by party leader Jo Swinson on Sunday, would involve Johnson ditching any attempts to push his withdrawal agreement bill through parliament before an election, something the government has rejected.

If it later became clear that the bill had stalled, Downing Street could agree an election without it, which could win the backing of enough opposition MPs to pass.

The timetable would be extremely tight. Given the legally mandated five-week delay between the dissolution of parliament and an election, a plan would need to be in place in little more than a week to hold a poll on 12 December, the government’s preferred choice.

There could also be some jitters within the Lib Dems about giving up on a second referendum. Chuka Umunna, the former Labour MP who is now the Lib Dems’ foreign affairs spokesman, said this now did not seem possible without an election.

“It’s quite clear now that it’s highly unlikely that in this current parliament we’re going to be able to achieve that,” he told Sky’s Sophy Ridge on Sunday show. “It looks more likely that you would be able to do that in a new parliament.”

The change of stance has prompted agitation in the People’s Vote campaign, to which several Lib Dem MPs are allied, with some understood to be not entirely happy at the move.

But one senior Lib Dem said there seemed to be no option: “We would prefer a people’s vote but Labour have consistently failed to deliver enough troops to win that fight and, with 19 Labour MPs voting for Johnson’s Brexit bill, we can’t wait around till Labour get their act together, if they ever will.”

The government has so far avoided seeking an election via a bill because these can be amended, with MPs potentially imposing conditions such as votes for 16- or 17-year-olds, or allowing EU nationals to vote in general elections.

The Downing Street hope would be that if Johnson gave categoric assurances about a fixed election date, thus ruling out the possibility of a drift into a no-deal Brexit, the opposition parties would pledge not to table any amendments.

However, the near-complete lack of trust between the factions in the Commons could still scupper such a plan.

The immediate focus will be in the Commons on Monday afternoon, where Johnson will challenge Labour to support an election via the FTPA motion.

The shadow home secretary, Diane Abbott, said only a promise from Johnson to MPs would suffice.

“He could come to parliament and categorically give parliament an undertaking that he’s not going to come out without a deal,” she told BBC One’s The Andrew Marr Show.

While Abbott said she would welcome a campaign – “We have over half a million members and they want an election” – the sentiment is not unanimous in the party, with many MPs and a number of shadow ministers wary about agreeing to an election, given recent polls showing the Conservatives taking a lead of up to 16%.

One senior MP said Labour’s coherence on the issue could be tested if the EU agreed to a 31 January extension: “I get the impression we have quite a unified position as things stand. If the EU granted a long extension, that may change,” the MP said.