There is renewed attention on the prime minister's push for closer relations with Europe - and that is causing ripples in his own party and others.
Andy Burnham told his Cabinet earlier this week: "I firmly believe we have ended up with a harder Brexit than people voted for… no sensible person thinks the deal negotiated by the Tories is working for the country."
It comes ahead of a week which will focus minds on the UK's relationship with the bloc. On Thursday, at a gathering of European leaders in Dublin, Burnham will for the first time meet those who could prove pivotal as he sells his vision for Britain's future in the bloc.
And next week, he will deliver a speech on foreign policy, in which – for Burnham – Europe is a central plank. He will then travel to Brussels for a UK-EU summit to sign new agreements on food, energy and youth mobility.
Talking about the new deal to be signed at the summit, Burnham said to ministers: "We will take opportunities that make people in this country better off.
"There is a significant prize."
Brexit referendum 'possible' in Labour election manifesto, says Burnham
UK and EU agree draft deal to scrap Brexit red tape over food exports
This lies behind the prime minister's decision to open the door to the argument about rejoining the EU single market - along with the freedom of movement that would bring - and even the EU altogether.
But that longer-term ambition is dividing his cabinet and his party.
Some welcome his approach, including those with formerly Brexit-backing constituencies. Angela Rayner, for example, is understood to have been pushing former Prime Minister Sir Keir Starmer to be bolder on Brexit since at least autumn 2022.
The housing secretary is said to have been insistent that Labour needs to stick to its manifesto red lines – not to return to the EU single market, customs union, or freedom of movement – but is open minded to changing those at the next election.
Another cabinet minister said: "The best thing you can do in politics is tell the truth. And the truth is that Brexit has been hugely damaging to Britain.
"We are not leading a public conversation here, we are racing to catch up with the public."
But others are watching nervously at a strategy one former minister described as "high risk".
Home Secretary Shabana Mahmood, for example, has struck a more cautious tone warning about the "costs and consequences" of rejoining the EU as well as staying out.
Jonathan Reynolds, the Business and Trade Secretary, is supportive of getting closer to the EU and discussing the UK's long term relationship.
But he has previously warned against joining the EU's customs union and is also unsure about the prospect of rejoining the EU, highlighting the uncertainty of what terms the UK would face, and what the bloc could look like in years to come with nationalist parties in the ascendancy in several European countries.
A voice from the past has a different set of concerns.
Lord Cameron told Bloomberg's Mishal Husain that starting a conversation about rejoining would be "very long and painful".
The former prime minister warned "flirting with rejoining" could also harm Burnham's attempts to renegotiate the Conservative's Brexit deal.
"If you start endlessly producing this idea that we're actually on a path to rejoining, I think you're in danger of getting a less good partnership deal because of course the EU countries will just think: 'Well, these guys are gonna rejoin anyway, so what's the point in giving them a good partnership deal'."
Attitudes in Labour towards the prime minister's approach don't divide along predictable lines. One Scottish Labour MP, personally opposed to Brexit and with a heavily Remain-voting constituency, said it was a "real problem".
"How can I argue to my constituents that we had a Scottish referendum in 2014 that settled independence for a generation. but then say the 2016 referendum isn't settled? My view is you accept democracy."
For now though, that opposition hasn't broken out into public rebellion, although Labour MP Gareth Snell is one who has warned about reopening the debate.
The MP for Stoke-on-Trent, where the Leave vote was 69.4%, told the BBC's Westminster Hour that doing so would "monopolise an awful lot of time inside parliament, inside government" when there are other things MPs should be doing.
Two Labour MPs among those most unhappy about Burnham's openness to Europe insisted "there are no plans" for any organised criticism of the prime minister.
Despite their concerns, particularly about free movement, they described their current mindset as "wait and see". That temporary truce is likely to fracture if the prime minister's lead in the polls begins to slide.
Badenoch has pledged that a future Conservative government will withdraw the UK from the European Convention on Human Rights (ECHR)
But Burnham's strategy has left other parties struggling to react.
The Conservatives have strongly opposed any move to align with EU rules into the future, with the party leader Kemi Badenoch saying that would be a red line and "actually take us backwards".
But some Conservative MPs are beginning to express unease about the strategic dilemma presented for their party by Burnham's moves on Europe, fearing that the issue could again divide Conservative voters.
In recent months Badenoch and her team have intensified efforts to win back affluent voters, especially in the south of England, who view Burnham's economic offer as too left-wing.
"The problem is that some of those voters are only just giving us a hearing again after Brexit," one Conservative MP said, "and now they are going to keep being reminded of it."
The Liberal Democrats have enjoyed being the most pro-European of the largest parties in Westminster. But some Lib Dems now fear their distinct position risks being drowned out by Burnham.
Reform UK though say they are "very bullish" about the return of Brexit to political debate, despite polling that suggests public sentiment has shifted since 2016.
"If he [Burnham] wants to fight an election on a £40bn bill to rejoin, open door immigration, and less control over our laws and our courts then we are very up for that," a Reform UK strategist said.
The party believes that just as it would build a progressive anti-Brexit coalition around Labour, it would also unite Brexit supporters around Reform UK as the most anti-EU party.
Get in touch
What questions do you have?
Sign up for our Politics Essential newsletter to keep up with the inner workings of Westminster and beyond.
