Andy Burnham was plunged into a fresh row over his Brexit beliefs on Saturday night after it was revealed the Government is pushing for Britain to be readmitted to a new version of the EU single market.

The Manchester mayor – a Remain supporter trying to win a by-election in pro-Brexit Makerfield – was challenged to say if he would continue with his stance if he replaced Sir Keir Starmer as Labour leader and Prime Minister.

Mr Burnham sought to dodge the Brexit issue last week by saying there was a 'long-term' case for rejoining the EU but he wouldn't be making it 'in this by-election'.

But on Saturday night Tory trade spokesman Andrew Griffith called on him to come clean on what he would propose to Brussels. Mr Griffith said: 'Whether Burnham likes it or not, Brexit is the elephant in the room in this by-election.

'On something as profound as to whether the Parliament he wants to be elected to should decide our own laws rather than hand them to Brussels, he must get off the fence. No supposed "straight talker" can fudge this for the next four weeks.'

The spat broke out after it was revealed Michael Ellam, Britain's chief negotiator in 'reset' talks with the EU, had offered to align the UK with EU regulations to allow free trade in goods with the bloc.

The move, proposed in the next phase of the Government's Brexit reset, emerged last week after the Prime Minister vowed 'this Labour Government will be defined by rebuilding our relationship with Europe, by putting Britain at the heart of Europe'.

Brussels is understood to have responded by suggesting the UK join the customs union or allow the return of freedom of movement – both explicitly ruled out in Labour's 2024 General Election manifesto.

Cabinet Office sources said on Saturday a 'range of options' had been presented to the EU, whose diplomats are said to be reluctant to give 'preferential treatment' to the UK after the tumult of Brexit.

Mr Burnham, 56, said last year he hoped to see the UK rejoin the EU 'in my lifetime'.

But while fellow leadership hopeful Wes Streeting appeared happy to put the issue centre-stage by calling for Britain to rejoin, Mr Burnham said: 'In the long term there is a case for that, but I'm not advocating that in this by-election.'

On Saturday night Mr Burnham's camp fought shy of addressing the issue again, with a source saying: 'His focus is solely on the by-election.'

Makerfield, near Wigan, voted 65 per cent for Brexit in the 2016 referendum – which Reform leader Nigel Farage said he would highlight in his by-election campaign.

Sir Keir tried to neutralise Brexit as an issue by setting 'red lines' in Labour's 2024 election manifesto by ruling out rejoining the EU, the single market or a customs union in his lifetime.

The proposal by Mr Ellam comes ahead of a UK-EU summit set for July. The Government is preparing to announce closer ties with the EU on youth mobility and trade in farm products.