According to analysis carried out by motoring research charity the RAC Foundation, this is the same as a claim being made every 17 minutes - here's how to claim for pothole damage.
But the research, which is based on data from 204 local authorities, shows that councils paid out for the claims in only around a quarter of cases.
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The average value of a claim was £432, but the average pay-out was just £306.
Hampshire was the council with the highest number of claims made against it at 1,952, followed by Surrey (1,412) and Hertfordshire (1,369).
RAC Foundation director Steve Gooding said: “These figures are symptomatic of the inadequate funding available for local road maintenance.
“Year in, year out, the backlog of work on local roads is estimated to run to several billion pounds.”
A survey of highway bosses in England and Wales by the Asphalt Industry Alliance found that it would cost £11.8 billion to repair roads to a reasonable standard.
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Mr Gooding went on: “A pitted road surface isn't just a problem for motorists - for those on two wheels it can be life threatening.
“Just last week the Chancellor acknowledged that there had been decades of underfunding in the nation's infrastructure and that he was keen to support targeted, value-for-money public investment.
“Providing the funds to fix our roads would be a great place to start and would show rapid results.”
Separate data from the RAC released earlier this year showed that the number of vehicle breakdowns caused by pothole-related damage has more than doubled over the last decade.
According to the figures, 0.9% of all call-outs received by the RAC in the year to June 2016 were for pothole-related breakdowns, up from 0.4% in the 12 months to June 2006.
Thousands of motorists require assistance each month for issues such as broken shock absorbers or faulty suspension springs, the RAC said.
Commenting on the latest research, Local Government Association transport spokesman Martin Tett said: “Current funding levels mean councils are only able to keep pace with patching up our roads and filling potholes rather than carrying out more cost-effective and long-term improvements.
“Long-term and consistent investment in local road maintenance is desperately needed to improve road conditions for motorists and cyclists.”