An RAC Foundation investigation found that 2,375 bridges spanning over 1.5m (5ft) were not fit to carry the heaviest vehicles, such as lorries of up to 44 tonnes.
It would cost about Â£328m to refurbish all affected bridges, the charity said.
The Department for Transport (DfT) said it was providing up to Â£1bn funding to English councils this year.
RAC Foundation director Steve Gooding said it was important for councils to keep their highway bridges up to scratch, and urged Chancellor George Osborne to provide more money for bridge maintenance.
"Councils are doing their utmost to keep their structures inspected, but where they find fault the price of repair can bust the hard-pressed maintenance budget," he said.
"We hope the chancellor has this in mind as he completes his spending review calculations this month."
The bridges deemed inadequate by the study represent 3% of the estimated 71,000 local bridges in Britain.
According to the research, which was carried out using Freedom of Information requests to 193 of Britain's 207 highways authorities and a survey of 50 councils, some of the bridges are substandard because they were built to less modern specifications.
It found others have deteriorated through age and use.
Mr Gooding cited the closure of London's Hammersmith Flyover, which was shut in 2011 for emergency repairs, as a "graphic illustration" of what could happen if national infrastructure is not maintained.
The flyover was closed following damage to cables in the structure, leading to major congestion.
A DfT spokesperson said funding due to be provided to local councils this financial year would "help repair local roads, including bridges and other structures."
Councils could focus on roads and infrastructure in need of urgent attention, they added.
However, a spokesman for the Local Government Association said councils are "stuck between a rock and a hard place", with traffic set to increase while local budgets are reduced.
More than 2,300 road bridge structures in Britain are inadequate, according to a new study.