Direct Line Insurance Group said it expects the three storms that lashed the UK last month will cost it up to £140 million in customer claims.
It said more than 200 claims advisers have so far inspected sites damaged by high winds and flooding caused by storms Desmond, Eva and Frank in December, which struck parts of Cumbria, Yorkshire and southern Scotland.
The insurer said it estimates claims will range between £110 million and £140 million, hitting both its home and commercial divisions.
Home claims from the storms are likely to be between £80 million and £100 million, compared with a normal annual level of claims from major weather events of about £80 million, the firm said.
Claims in its commercial unit are expected to be between £30 million and £40 million, which is between £15 million and £25 million more than in an average year.
However, the insurer said it still expects to hit its full-year existing combined operating ratio - a comparison of claims to premiums - of between 92% to 94% for claims from major weather events.
The announcement comes after estimates that last month's storm damage is likely to cost the insurance industry £1.3 billion.
The Association of British Insurers said just over 3,000 families are now in alternative accommodation, and so far the industry has paid out £24 million in emergency aid.
Almost 15,000 claims have been made for flood damage to property from homeowners and businesses, the ABI said. There are also thousands of smaller claims for storm damage.
The ABI said the average expected payout for each domestic flood claim is £50,000 - compared with an average from the 2013/14 winter storms of £31,000.
James Dalton, director of general insurance policy at the ABI, said: "In the immediate aftermath insurers have focused on urgent needs, providing families with somewhere to live and helping businesses into alternative trading premises.
"They get cash into the hands of those affected so they can buy food and dry clothes. Then they get the repair process under way as quickly as possible."
The ABI added that so far the industry has made more than 8,300 initial visits by loss adjusters, who handle the most severe claims.