Lib Dem leader Sir Ed Davey said such a move was a “no-brainer” for the prime minister, and would put “rocket boosters” on the UK economy and “strengthen our hand” with US President Donald Trump.

Sir Keir has ruled out rejoining the EU customs union and the single market, declaring it a “red line”.

But Labour has left open the possibility of joining another bloc, the Pan-Euro-Mediterranean (PEM) convention, as part of efforts to “reset” European relations.

PEM allows tariff-free trade of some goods from across dozens of countries in Europe, North Africa and the Middle East.

The Lib Dems say the UK should join it as a “first step” to rejoining the UK-EU customs union, which allows tariff-free movement of goods between EU member states – but prevents members striking their own trade deals.

The party’s ultimate aim is for the UK to rejoin the European Union – but it has only started campaigning on the issue since the general election.

Downing Street says Sir Keir’s meeting with EU leaders on Monday – the first time a British prime minister has been invited to such a gathering since the UK left the EU in 2020 – is focused on defence and security cooperation.

Ahead of an appearance on the BBC’s Sunday with Laura Kuenssberg programme, Sir Ed has written a letter to Chancellor Rachel Reeves calling for her to commission the Office for Budget Responsibility (OBR) to properly explore the impact a new customs deal with the EU would have on the UK economy.

The forecasts then should be made public as part of the OBR’s forecasts due to be published alongside the Spring Statement on 26 March, he wrote.

“The chancellor is tying herself in knots trying to think up new ways to grow our economy,” Sir Ed said.

“But there’s a solution right under her nose: a new UK-EU customs union deal that boosts trade for British businesses and raises vital tax revenue for our public services.”

Earlier this month, the EU’s new trade chief Maros Sefcovic told the BBC he was open to Britain joining PEM as part of a post-Brexit “reset”.

On the possibility of the UK joining the arrangement, the prime minister’s official spokesman has previously told reporters: “We’ve always said that we want to look at ways to reduce barriers to trade whilst remaining within our clear red lines.

“The arrangement that’s being discussed is not a customs union.

“Our red line has always been that we will never join our customs union, never re-join the single market, no freedom of movement, but we’re just not going to get ahead of those discussions.”

The Conservatives say joining PEM would turn the UK “into rule-takers and not rule-makers”.

Tory leader Kemi Badenoch accused the government of “trying to reopen the divisions of the past and edge us back into the EU”, after having “opposed us every step of the way” while the previous Conservative government brought the UK out of the EU.

She challenged Sir Keir to meet five tests that she said would ensure “he doesn’t undo Brexit”, which include: no “backsliding” on the free movement of people, or the compulsory transfer of asylum seekers, no new payments to the EU, and no reduction in fishing rights.

Badenoch also said Nato must have “primacy” when it came to European security – her final test.