Some 39% of motorists had their tyres, bodywork or other parts of their vehicles affected after hitting a pothole, the AA poll of 25,208 drivers found.
AA president Edmund King urged local authorities to “get to grips with fundamental road maintenance” such as poor drainage and crumbling surfaces.
He also called on the Chancellor to set aside extra funding to fix roads in next week’s Budget in order to “reverse the toll on vehicles and their owners’ pockets”.
The Local Government Association’s transport spokesman Peter Box warned that there is a £12 billion backlog in road repairs that would take councils “more than a decade” to clear.
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He added: “Councils fix more potholes than ever - one every 15 seconds - and keeping roads safe is one of the most important jobs we do.
“Current funding levels, however, and the size of the backlog mean they can only keep pace with patching up our roads and filling potholes.
“Long-term and consistent investment in local road maintenance is desperately needed.”
Transport Minister Andrew Jones said: “I know how important well-maintained roads are to people up and down Britain.
“That is why the Government is providing unprecedented levels of investment, allocating a record £6 billion to councils in England to improve local roads over the next five years.
“We topped this up with £250 million last year specifically to tackle the blight of potholes.”