The two likely challengers to British Prime Minister Keir Starmer for the leadership of the governing Labour Party and the country have begun to reveal their visions, including rejoining the European Union, were they to win the top job.

Last week was a bruising one for Starmer, who has been prime minister for less than two years, after the blame for hugely disappointing results in local elections was laid at his door, and as a result many Labour members of Parliament spoke of their opposition to his continued leadership.

One, Wes Streeting, resigned from his cabinet post as health secretary and has confirmed he will stand in any upcoming leadership vote, as will another leading light in the party, Andy Burnham, who is not currently an MP, and must become one before he can stand.

A Labour MP has said he will give up his seat to allow a by-election, which would give Burnham an opportunity to take his place. Burnham has already said that the party needs to acknowledge it "cannot carry on as we are", that it has "not been good enough" and "requires a lot of change".

"We've got to see this as a moment to reclaim the Labour Party, to save it from where it's been," he added.

In his resignation letter last week, Streeting called the local election results "unprecedented — both in terms of the scale of the defeat and the consequences of that failure", a clear nod to the growth in support of the far-right party Reform UK.

He added that "there is no doubt that the unpopularity of this government was a major and common factor in our defeats across England, Scotland and Wales", and that the country faced "big challenges that require a bold vision and bigger solutions than we are offering".

This summer marks the 10th anniversary of the 2016 referendum which led to the United Kingdom leaving the EU, the process known as Brexit, which still causes political and social division across the country. Both Streeting and Burnham have made a point of addressing the issue head-on in their early pronouncements.

Streeting called Brexit "a catastrophic mistake", which would one day be reversed, and spoke of the need for a closer relationship with Europe to help "rebuild our economy and trade, and improve our defense against the shared threats from Russian aggression and America First".

At last year's Labour Party conference, Burnham said he hoped the UK would rejoin the EU in his lifetime, but the constituency where he hopes to win a parliamentary seat is in an area where residents voted resoundingly to leave the EU.

When asked by ITV News if he still favored rejoining the EU, Burnham said "in the long-term there is a case for that", but he is "not advocating that in this by-election".