Chief executive Richard Ward told the Sunday Telegraph the London market has put in place a contingency plan to switch euro underwriting to multi-currency settlement if Greece abandons the euro.
Ward said the Lloyd's market, which is made up of around 80 insurance syndicates, could have to take writedowns on its STG58.9 billion ($A95.2 billion) investment portfolio if the eurozone collapses.
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Europe accounts for 18 per cent of Lloyd's STG23.5 billion of gross written premiums, mostly in France, Germany, Spain and Italy. The market also has a fledgling operation in Poland.
Ward told the newspaper: "I'm quite worried about Europe. With all the concerns around the eurozone at the moment, we've got to be careful doing business in Europe and there are a lot of question marks over writing business in the future in euros."
Ward said Lloyd's had been working hard on contingency planning and had the capability to switch settlement of European underwriting from euros to other currencies.
The contingency planning comes as German politicians piled the pressure on Greece ahead of elections on June 17.
The country's crisis deepened earlier this month after leaders failed to form a coalition government.
If an anti-austerity party is elected in June, many fear Greece will be denied further tranches of bailout cash and the country will have to exit the euro.
