The Lib Dems will urge Andy Burnham to end Labour’s “torpor and timidity” towards the EU as they call for the UK to rejoin the single market, in a notable strengthening of their own position.

Ahead of the 10th anniversary of the Brexit vote next week, Ed Davey will challenge Burnham to scrap Labour’s red lines on the customs union and single market if he becomes prime minister and immediately begin talks on a more ambitious deal with the EU.

He will argue on Wednesday for closer economic ties with the EU, even though that would include free movement, as well as a new European security council to counter mounting threats from Russia and the unreliability of the US president, Donald Trump.

It marks a significant step towards calling to rejoin the bloc. The Lib Dems took a more gradual approach at the last election, in contrast with 2019, when the words “stop Brexit” appeared in bold on the front of their manifesto.

Keir Starmer confirmed on Tuesday that the second EU reset summit would take place on 22 July, despite fears it could be postponed to the autumn with talks over youth mobility in deadlock. In 2024, Labour promised not to rejoin the EU, the single market or the customs union.

But in a major speech, Davey will say: “Labour’s red lines are holding Britain back. They are hurting the British people and they are playing into the hands of Farage and Reform.

“So my message to Andy Burnham, to Wes Streeting – to whoever the next prime minister may be – is this: drop those red lines. Drop them now, so we can move on from the torpor and timidity that marks out Labour’s approach to Europe so far.

“We can put an end to the endless talk of a ‘reset’, that so far seems to just mean saying ‘no’ more politely than the Conservatives did. And we can get on with properly fixing our relationship with Europe.”

Davey will argue that the Lib Dems’ plan to join the single market as a member of the European free trade agreement – alongside Norway and Iceland – and form a new UK-EU customs union would fully remove trade barriers to Europe and reverse years of economic damage from Brexit.

It would represent “the best hope our country has to stop the chaos and end the crisis – and the biggest step we can take back towards membership of the EU”, he will say.

“People are fed up … They know the hard truth that most politicians won’t admit: the Conservatives’ Brexit experiment has failed. And it’s failed all of us. £90bn a year – that’s how much it’s costing us all.”

A return to the single market would require the UK to accept free movement, putting Davey on a collision course with the Tories and Reform UK over immigration.

EU officials have said they are open to the UK joining the European Economic Area – the European single market – but have ruled out a British proposal for common rules on goods without free movement of people.

Charles Michel, a former European Council president, told the Guardian that the EU single market was “not for sale” when asked about the British proposal of a single market for goods. “If the dream in the UK is to build closer ties, but if the consequence is less integrity in the single market, that will not work, because I feel that the single market is not for sale.”

He said the UK’s wish “to take the advantages of Brexit … without having any constraints” was not new and had been demonstrated throughout the Brexit negotiations.

Michel, who was Belgium’s prime minister at the time of the 2016 referendum, said he expected the EU would react with “a positive spirit” if the UK ever decided to rejoin. He emphasised this was a question for UK politics “if and when there is the readiness for a serious domestic debate”.

Lib Dem party sources argued that Brexit had led to the “Boris wave” and small boats crisis, suggesting the UK could negotiate a “very tight” returns agreement under the Dublin framework, while sectors including hospitality, agriculture and social care would benefit from more EU workers.

The party is also calling for much deeper defence cooperation with the EU to help guarantee UK security, including the establishment of a European security council and a new rearmament drive to improve the continent’s ability to deliver Nato’s operational requirements.

The party, which has 72 MPs, believes the UK could use its defence prowess as a bargaining chip with Brussels to negotiate a better deal, with some EU members already hoping to go further on military cooperation, alongside – rather than instead of – their Nato commitments.