Wes Streeting plans to drag Britain back into the EU if he becomes Prime Minister – shattering Labour's claim it would respect the 2016 Brexit vote.The former Health Secretary put the bitterly divisive issue at the heart of his campaign to replace Sir Keir Starmer as he formally announced his leadership ambitions on Saturday.While the Prime Minister was at Chequers sketching out what sources called an 'orderly timetable' for his resignation, Mr Streeting was describing Brexit as 'a catastrophic mistake'.He added: 'Britain's future lies with Europe – and one day back in the European Union' – in a comment that will turn the political screw on leadership rival Andy Burnham.The Manchester mayor is also pro-Europe but will not want any focus on the issue as he tries to win a by-election in the Makerfield constituency – which voted 65 per cent for Leave in 2016 – as he embarks on his own leadership challenge.And on Saturday, Mr Burnham already appeared to be on the back foot over the key issue when he was asked by ITV News if he was in favour of rejoining the EU.The mayor, who has previously said he hopes the UK will rejoin 'in my lifetime', replied: 'I've said in the long-term there is a case for that, but I'm not advocating that in this by-election.'Mr Streeting's remarks were described by government sources as 'divisive' and 'pure, selfish ambition', while Reform UK's leader Nigel Farage told The Mail on Sunday: 'The North will be lost to Labour forever.' Wes Streeting called Brexit a 'catastrophic mistake' on Saturday as he confirmed he would stand if a Labour leadership election were calledAndy Burnham is aiming to return to Westminster at the Makerfield by-election, where constituents voted 65 per cent for Leave in 2016Tory chairman Kevin Hollinrake said: 'While Labour relitigate Brexit, Britain is not being governed.'Mr Streeting's resignation as Health Secretary in protest at the 'vacuum' in No 10 came during a tumultuous week for Labour following their disastrous local election results.MP Josh Simons announced he would stand down as Makerfield MP, with Mr Burnham, immediately declaring he would stand. And fellow leadership hopeful Angela Rayner was effectively cleared to run too, after HMRC told the former Deputy Prime Minister she would not be fined for underpaying stamp duty on her seaside home in Hove.However there is growing resistance among Labour MPs to the idea that Mr Burnham – the so-called 'King of the North' – could succeed Sir Keir in a 'coronation'.Mr Streeting responded to those fears by saying: 'We need a proper contest with the best candidates on the field, and I'll be standing.'In his first public speech since quitting government, he also addressed the threat from Reform, saying: 'The voters did more than send Labour a message last week, they issued a warning: that unless we change course, we risk being the handmaidens of Nigel Farage and the breakup of the United Kingdom.'In another dramatic day at Westminster:Sources told the MoS that Sir Keir wanted to leave No 10 'in a dignified way, and in a manner of his own choosing' by 'setting out a timetable' – despite his former chief of staff Morgan McSweeney urging him to 'hang on';Mr Burnham told BBC News that his ambition was to 'save' Labour, saying: 'We can't just carry on as we are';A snap poll of Labour members who will choose their leader – conducted by pollsters Find Out Now for the MoS – put Mr Burnham streets ahead of both Ms Rayner and Mr Streeting.Mr Streeting told supporters at a Progress think-tank event on Saturday: 'The biggest economic opportunity we have is on our doorstep. We need a new special relationship with the EU, because Britain's future lies with Europe.'Last night, senior Labour MPs condemned the idea that Mr Burnham could be crowned leader without a vote of the rank-and-file members. Bermondsey MP Neil Coyle, who branded the Manchester mayor a 'nightmare for the Labour party', told the MoS: 'Andy Burnham's sense of entitlement is astonishing. 'He may revel in his King of the North nickname but he forgets that most Labour members are republicans at heart.' Sources told The Mail on Sunday Sir Keir Starmer wants to leave Downing Street in a 'dignified' mannerVeteran Labour backbencher Clive Efford added: 'A coronation would be a huge mistake – we need a contest. We had a coronation when it was Gordon Brown [taking over from Tony Blair], and as much as I backed him, it undermined him all the time that he had not faced a contest and been elected.'And former minister Graham Stringer said: 'The Labour Party has a democratic constitution that cannot be thrown to one side.'But one senior Labour source suggested Mr Burnham could become leader without a contest if he beat Reform UK in Makerfield by more than 2,000 votes on June 18 – the 201st anniversary of the Battle of Waterloo. But the source stressed it would have to be a 'decisive victory', adding: 'He must not just slay the Reform dragon – he must slaughter it! Anything less, and I don't think Andy will have the momentum for a coronation.'MPs also voiced concern about whether Sir Keir should announce a timetable to quit. Mr Efford warned it would be 'premature' before the Makerfield by-election. He said: 'I don't think a change of leader in the short term is what we need. We need to steady the ship then we can talk about a transition if that's what's needed.'Mr Burnham also came under fire from some Labour members for allegedly not mentioning he was brought up in a prosperous Cheshire village. One, posting on a Labour WhatsApp group, said: 'AB grew up in a large, five-bed house in the poshest part of that area – not the terraced streets or council estates of Makerfield'.Mr Burnham, who until 2017 was MP for the neighbouring constituency of Leigh, insisted he was no 'carpet bagger' and had a 'connection' with the seat.He told Channel 4 News: 'I live on the edge of this constituency. My kids went to school a few hundred yards down the road. I know people here, I know how they think, how they feel.'I want to do whatever I can to make Labour a party that they can believe in again – a party that's solidly on the side of working-class people.'Last night, Reform UK leader Nigel Farage seized on Mr Burnham's discomfort, saying: 'He has favoured rejoining for some time and we will remind voters every day.'