“For the first time any consumer in the U.S. and the U.K. will be able to beam sterling and dollars back and forth, instantly for free,” said Jeremy Allaire, the co-founder of Circle. “That’s just never been possible.”

It is a difficult moment for the virtual currency. The developers who maintain the basic Bitcoin software have been divided over updates to the software. That has caused a schism in the Bitcoin community and slowed down transactions.

Some companies have been looking at other virtual currencies, such as Ethereum, as an alternative way to transfer money using what is known as a blockchain, the database concept that Bitcoin introduced. Mr. Allaire said that Ethereum was not yet ready for global use in the same way as Bitcoin, but that it could be in the future.

“We are not wedded to one blockchain as the right one,” he said.

In the United States, Circle has not managed to take Bitcoin mainstream, but it has gotten Bitcoin some key seals of approval. Back in 2013, it got funding from the major venture capital firms Accel Partners and General Catalyst Partners. And last year, Circle became the first company to get a so-called BitLicense from New York state’s top financial regulator, the Department of Financial Services.

The New York agency had been the only regulatory body to devise a licensing system for virtual currency companies, trying to confront the fraud and crime that have plagued the technology.

But the British government has taken several steps to emphasize its interest in attracting virtual currency start-ups, among other types of financial technology, to London.