Though video conferences can substitute for many face-to-face meetings, the Brexit talks are complex, ranging over an array of issues, from fisheries to finance, and involving a British negotiating team of 100 officials. Given the grim arithmetic of the pandemic, several of those negotiators are likely to fall ill.

“It would be better to agree a delay now,” Mr. Henig said. “If June is the peak of the virus and it is also the point where we are going to say, ‘no further extension,’ then that starts to look like a lack of forward planning.”

Analysts noted that coronavirus could give Mr. Johnson political cover to ask for an extension, if that was what he wanted to do anyway. Last fall, the prime minister cited a law passed by Parliament as giving him no choice but to ask for the withdrawal deadline to be moved from October to January.

For Mr. Johnson, however, such a move poses a dilemma. Under the terms of its agreement, Britain would be required to pay billions of pounds to the European Union if it continued to have access to the single market and customs union beyond the transition period that ends in December.

That would be an acute embarrassment for Mr. Johnson, damaging him particularly with the hard-line Brexit wing of his Conservative Party. Pro-Brexit forces have already begun campaigning against a delay — suggesting, in a strategy that echoes some defenders of President Trump in the United States, that these calls were part of an effort to exaggerate and politicize the virus for partisan ends.

“The same people who wanted to stop Brexit now want to extend the Transition Period, ostensibly over Coronavirus,” said the Bruges Group, a Euroskeptic research institute, on Twitter. “We know the pattern: Any excuse is found, one delay turns into another and Britain ends up in political purgatory. Brexiteers won’t fall for this.”