Markel reported gross written premiums up by 21% in the first half to $1.3bn from $1bn in the same period last year.
Overall, the group's net income was $9.66 a diluted share for the six-month period, compared to $4.09 last year.
Its London Market operation both increased its volume and improved its combined ratio, but remained above 100%, signifying an underwriting loss.
Gross written premiums in the London Market increased by 12% to $366m by 30 June, up from $326m in the same period the year before.
Earned premiums in the London Market increased by 9% to $264m from $242m.
Markel International finance director Andrew Davies said that the rise in GWP reflected growth in professional indemnity (PI) and retail operations.
The PI book in particular saw rate increases of more than 30%. Davies forecast the hard conditions were set to continue for the rest of the year.
The London Market combined ratio improved to 102% in the six months from 109% in the same period last year, and also hit 102% in the second quarter from 103% in the first quarter.
Davies said the fact that it was still over 100% - compared to a consolidated group total of 96% in the six months, against 102% last year - reflected Markel's conservative reserving policies.
He hoped it would be below 100% by late this year or the first half of next year.
The factors driving the ratio down were reported as being better risk selection and pricing, appropriate use of reinsurance and lower expenses.