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Mayor of London Sadiq Khan is set to attack what he will describe as the government's "denial" of the "immense damage" he says Brexit is doing.
In a speech at Mansion House in the City of London, he will call for a shift to greater alignment with Europe.
The Labour mayor is expected to say the consequences of leaving the EU "can't be airbrushed out of history".
In contrast, Sir Keir Starmer has ruled out rejoining the EU single market if Labour wins power.
In November, Chancellor Jeremy Hunt ruled out a revised trade deal with the EU, after reports he wanted the UK to have a Switzerland-style relationship, with closer alignment with EU rules and fewer restrictions on migrants.
In a speech to London's business leaders, Mr Khan will say: "I simply can't keep quiet about the immense damage Brexit is doing.
"Ministers seem to have developed selective amnesia when it comes to one of the root causes of our problems.
"Brexit can't be airbrushed out of history or the consequences wished away."
He will point to the economic effects of Brexit, and argue for a new approach to "sensibly and maturely mitigate the damage that's being inflicted".
In October 2021, the independent Office for Budget Responsibility estimated that Brexit would reduce UK GDP [economic output] by 4% a year.
The government says the trade deal struck with EU in December 2020 is "the world's largest zero tariff, zero quota free trade deal".
"It secures the UK market access across key service sectors and opens new opportunities for UK businesses across the globe.
"Despite difficult global economic headwinds, UK-EU trade is rebounding, with recent data showing that UK trade to both EU and non-EU countries is above pre-Covid levels".
In his speech, Mr Khan will say: "After two years of denial and avoidance, we must now confront the hard truth: Brexit isn't working.
"It's weakened our economy, fractured our union and diminished our reputation. But, crucially, not beyond repair.
"We need greater alignment with our European neighbours - a shift from this extreme, hard Brexit we have now to a workable version that serves our economy and people."
He will acknowledge that "no one wants to see a return to the division and deadlock" of recent years, but call for a "pragmatic debate" about the benefits of the EU's customs union and single market.
'Take back control' bill
While the mayor's criticism is aimed at the government, it will also be seen as a swipe at the recent harder stance on Brexit taken by his party leader.
Like Mr Khan, Sir Keir campaigned for Remain in the 2016 referendum and later for a second referendum.
But he has recently ruled out bringing back the free movement of people and argued there is no case for rejoining the single market.
Instead, he said Labour would fix the holes in the government's Brexit deal to "make Brexit work" - including a "take back control" bill devolving powers from Westminster to local communities.
Asked if Mr Khan's comments were helpful, Labour's shadow attorney general Emily Thornberry told the BBC: "It's our job to make Brexit work.
"We're not going back into the European Union... What we now need is a decent relationship with our closest neighbours with whom we trade and do most of our trade, and we need to have a grown-up relationship and not be shouting at them, but sitting down and negotiating properly and finding compromises, and finding a way through."