The Liberal Democrats will try to push MPs to a fresh vote on a second Brexit referendum next week.

The party has tabled an amendment to the Queen’s speech requesting that any deal brought back from Brussels by the prime minister is put to another public vote.

The Lib Dem leader, Jo Swinson, said: “The Liberal Democrats are the strongest party of remain and have been the leading voice in the People’s Vote campaign.

“Boris Johnson is determined to have a general election, but the best way to resolve the Brexit chaos is to have a people’s vote and give the British people the final say about their future.

“The best deal we have is as members of the European Union and we want to give the people the chance to choose to stop Brexit.”

Johnson’s legislative agenda was set out on Monday during the state opening of parliament. MPs are now in the midst of five days to debate on the Queen’s speech – which contained 26 bills – and will vote on whether to pass it early next week, possibly Tuesday.

With no majority and the expectation that Labour and the SNP will vote it down, the government is likely to struggle to get it through parliament.

The amendment brought by the Lib Dems if selected by the Speaker could be a significant moment in the Commons as it is another chance to show whether there is a majority for a second referendum. Another referendum on Brexit was rejected during indicative votes held in April.

The Lib Dems have said they back another vote on EU membership but, should they win a majority of seats at a general election, they would immediately revoke the government’s decision to trigger article 50 and the UK would remain in the bloc.

They have weathered significant criticism amid claims the party’s position is undemocratic. However, Swinson has stated that revoking article 50 is the right course of action because a no-deal Brexit would be like “burning your house down”.

MPs who support a second Brexit referendum believe they are nearing a majority, but they remain apprehensive as it would involve winning over many of about 40 Labour MPs who either opposed or abstained on the issue at the last parliamentary vote.

Ruth Smeeth was one of four MPs from heavily leave-backing constituencies who defied the Labour whip in order to vote against a second referendum. She quit her frontbench role, working for the deputy Labour leader, Tom Watson, saying that Britain “needed to leave, and leave with a deal”. Smeeth argued that her position was what was best for her constituents in Stoke-on-Trent North.

On the last numbers, around 330 MPs were against a second referendum, with 292 in favour. However, pressure has been put on Labour MPs to change their positions in light of the party’s clear policy in favour of a referendum on a Labour-negotiated deal.