LONDON—Two big British asset managers blocked worried investors from pulling money out of real-estate funds, and the pound sank to a new 31-year low Tuesday, twin signs that the U.K.’s vote to leave the EU was injecting new turbulence into financial markets after days of relative calm.

At the same time, the Bank of England eased regulatory restraints on British banks, a bid to allow them to lend more and keep the economy flush with credit.

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