LONDON — He is the bane of bankers, a bearded, teetotaling socialist often derided in the British press and in Parliament for his efforts to suppress dissent inside the Labour Party and his radical plans to remake the British economy.

But in the unmitigated chaos of Brexit, Jeremy Corbyn, the opposition Labour leader, is trying to remint himself as a safe pair of hands, and an unlikely salve to jittery British markets panicked by Prime Minister Boris Johnson’s plans for an abrupt split with the European Union.

And, surprisingly, it might be working.

“‘What method of execution would you prefer?’ is basically the question,” said David Willetts, a Conservative former minister who was once an aide to Margaret Thatcher. “Corbyn would in normal circumstances look like an off-the-scale risky gamble. However, Brexit is the single biggest change in Britain’s economic and political relations in 40 years, so Brexit itself is an off-the-scale economic gamble.”

With an early election looming, Mr. Johnson’s Conservative Party, once a friend to big business and a refuge for establishment figures of all types, has torched one convention after another, creating dust-ups with Queen Elizabeth II, the Supreme Court and Parliament. The prime minister’s proposed Brexit deal, proffered last week to Brussels, was met with so much dismay that most analysts believe he is fully resigned to Britain leaving the bloc without one.