Cornhill's premium income increased by 14.4% in the first half of the year to E1.4bn (£895m).
The result was achieved by higher commercial property premiums and the strength of the UK motor market.
Cornhill parent group Allianz also saw its net income increase by 15.1% in the first six months of the year to E1.6bn (£1.03bn).
Cornhill's expense ratio improved to 30% from 31.7%. But falling investment income took its toll.
Company spokesman Geoff Mayhew said stock market losses were "factored into our rate calculations".
The company's trading performance in the first half was strong, he said.
He added: "The major influence at the moment is getting commercial rates up to economic levels."