About 99% of motor insurance claims are successful, according to industry figures.
The Association of British Insurers (ABI), which analysed claims made in 2014 and 2015, said payouts were made in all but 1% of private motor insurance claims. The average payment was £2,347.
Meanwhile, about 84% of home insurance claims made across 2014 and 2015 were successful. The figure has increased from 79% in 2013-14 and the ABI said this reflected efforts to increase customer awareness about what might or might not be covered. The average home insurance claim paid out is now £2,627.
And nearly nine in 10 (87%) of customers claiming on their travel insurance received a payout in 2014-15. The average payout on this type of insurance was £880 - but the ABI said claims could include very expensive medical bills, sometimes higher than the cost of the average UK house.
Overall, more than 9,000 claims were paid every day during 2014 and 2015. They resulted in payments totalling £20 million being made to customers every day.
Huw Evans, the ABI's director general, said: "Insurers know that paying a genuine claim is the acid test for most customers. Being open and transparent about just how many claims get paid is vital to rebuilding trust and ensuring customers understand what their insurance policies cover.
"The ABI has worked with our members to ensure customers of motor, home and travel insurance now know how likely their claim is to get paid.
"Insurance customers should take confidence that the vast majority of all claims are paid, providing peace of mind and greater security to our millions of customers."