Workers count ballots in Islington, London on June 23, 2016 after polling stations closed in the Brexit referendum. REUTERS

Ten years after Britons voted to leave the European Union, a broad consensus has emerged that Brexit has weakened the United Kingdom's economy and international influence, even as the prospect of reversing it remains politically remote.

The reevaluation of the nation's decision to leave the bloc has set up the tantalizing prospect of the UK eventually rejoining the EU, a possibility that gained a foothold when Andy Burnham took over as the UK's new prime minister on July 20.

Burnham, a believer in the importance of the UK being part of the bloc, has ruled out an immediate rerunning of the 2016 referendum that precipitated the country's exit. But it seems highly likely he will take the country closer to the bloc than it has been at any time in the past decade.

And the relations between Brussels and London took a step forward this week when European Commission President Ursula von der Leyen messaged Burnham to say she looked forward to working with him for the "prosperity of people on both sides of the (English) Channel".