It may be some time before London market insurers find out how Britain’s vote to leave the European Union will affect their business, but several big names in the market appear to be hoping for the best but planning for the worst.

Lloyd’s of London and at least two of the largest insurers in the market say they are looking at setting up operations in other E.U. countries to ensure that they can continue to write business across the trading and political bloc after Britain leaves.

The key issue, which the insurers hope will be resolved in their favor in the so-called Brexit negotiations, which are expected to begin next year, will be whether U.K. insurers will retain “passporting” rights, where an insurer licensed in one E.U. country can write business in all others.

If U.K. insurers don’t retain that right, they will have to go through what will likely be the lengthy process of establishing operations in the E.U. Lloyd’s, which as a market houses the London operations of numerous insurers, said it is looking at various locations — including Dublin, Paris and Frankfurt, Germany — where it might set up a hub to enable it to continue to passport business.

In announcing the market’s half-year results last month, Lloyd’s Chairman John Nelson said the market is making plans to continue to write business throughout Europe. “Our aim is to have a contingency plan in place so we can write business anywhere in the E.U.” by the time Article 50 of the Lisbon Treaty, the mechanism by which a country leaves the bloc, is triggered, Mr. Nelson said.

“We will continue to analyze the 30 countries in the European Economic Area and the full range of options available to us,” Lloyd’s said in a statement.

Both Mr. Nelson and Lloyd’s CEO Inga Beale stressed, however, that Lloyd’s will remain based in London.

Beazley P.L.C., which operates syndicates 623 and 2623 at Lloyd’s, is examining the possibility of gaining an Irish license for its E.U. reinsurance business and of setting up an E.U. insurance company, the insurer’s CEO, Andrew Horton, said earlier this year.

Beazley, which relocated its headquarters to London from Dublin before the U.K. referendum on E.U. membership in June, has retained a subsidiary in Dublin.

And Bronek Masojada, CEO of Hiscox Ltd., which operates syndicate 33 at Lloyd’s, said the Hamilton, Bermuda-based insurer and reinsurer is examining E.U. jurisdictions where it already has offices as possible locations for a subsidiary, as well as Malta and Luxembourg.

Considerable uncertainty remains about the access U.K.-based insurers will have to the European single market once the country leaves the E.U.

Lloyd’s and other London market bodies have said they will lobby legislators for the U.K. to retain passporting rights.

But some other London insurance market companies are “not prepared to wait” and already are examining the options open to them if passporting rights are not retained, said Stephen Netherway, a partner at law firm CMS Cameron McKenna L.L.P. in London.

Others, however, will “wait and see” if the outcome of Brexit negotiations — which likely will take some time — are advantageous to them, he said.

Setting up such an operation could take up to 18 months or two years, which is why some insurers are establishing plans now, he said.

If London market insurers opt to set up operations in other E.U. territories, risk managers should be aware of the potential for confusion over jurisdiction and governing law in the case of disputes with their insurers, said Richard Mattick, who is of counsel at law firm Covington & Burling L.L.P.

While many insurance policies contain governing law or jurisdiction clauses, many do not, which could “prove tricky,” particularly where business is written on a subscription basis with several underwriters on a slip, Mr. Mattick said.