Admiral's shares fell 7.7% after it said falling interest rates since the referendum had affected its solvency ratio, although it stressed the ratio "remains strong".
Its shares were the worst performers on the FTSE 100, with the index closing down 34.77 points at 6,859.15.
Admiral also cited other risks to its business following the Brexit vote.
These include interest and exchange rate volatility, and the possible withdrawal of passporting rights that allow UK financial services firms to trade in Europe.
Admiral's comments overshadowed the news that its pre-tax profits increased by 4% to £193m for the six months to 30 June.
Balfour Beatty shares rose 3% after the construction company restored dividend payments and said it was seeing "tangible benefits" from its turnaround plan.
The company reported a pre-tax loss from continuing operations of £21m, compared with a £150m loss a year earlier.
On the currency markets, the pound was given a temporary boost by slightly better-than-expected UK jobs figures. But the effect soon wore off, with sterling down 0.3% against the dollar at $1.3001 and 0.2% lower against the euro at €1.1543.
(Close): Shares in car insurer Admiral dived after the company said it had taken a hit from the Brexit vote.