Insurance market Lloyd's of London is working on "contingency plans" to ensure it can trade across Europe when the UK leaves the EU.
Chief executive Inga Beale told the BBC that Lloyd's may set up a subsidiary or branches in mainland Europe.
She estimates that 4% of revenues could be lost after Brexit because Lloyd's would lose its licence - or passporting - rights to operate across the EU.
The fallout from Brexit "is a major issue for us to deal with", she said.
Lloyd's, one of Britain's oldest institutions, is the world's leading insurance and reinsurance market and houses around 90 syndicates. It focuses on specialist markets, such as marine, energy and political risk, and this year insured the taste buds of a Cadbury's chocolate taster.
Continental Europe accounts for about 11% of gross premiums written by the London market. Ms Beale told the BBC that Lloyd's was now "focusing our attention" on maintaining its position in a post-Brexit landscape.
It had not yet been decided whether to establish branches in individual EU countries or an EU-wide subsidiary, but the latter option would probably be cheaper, she said.
But Ms Beale said Lloyd's had to respond. "It's the lack of certainty for our clients. Business cannot hang around," she said. "Boards are going to insist that they make plans [for life after Brexit]"
She did not disclose details of the size of any EU-based subsidiary or consequences for jobs, but said: "Some people may end up doing their jobs in other parts of Europe rather than in London."
Despite the rise, premiums continue to be under pressure, said Lloyd's chairman John Nelson.
He said: "Whilst we are operating in difficult conditions, we have continued to make significant progress in growing our presence in the fast-growth markets across the globe.
"In 2016 we have applied for onshore reinsurance licences in India and Malaysia as well as opening a new office in Bogota, Colombia. This complements the growth we are seeing in Dubai, China and in our more traditional markets, particularly the United States."