The Association of British Insurers say drivers need to be able to prove that they're not at fault if the technology goes wrong.
It wants to collect data covering 30 seconds before and 15 seconds after a collision, revealing the location and whether the vehicle was in autonomous mode.
ABI director general Huw Evans said the information "would offer public reassurance by protecting motorists from being incorrectly blamed if something fails with their car, helping police investigations and supporting prompt insurance payouts”.
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On occasions where faulty technology was shown to have caused an accident insurers should be able to recover the costs from the manufacturer the ABI says, helping keep insurance premiums down.
The UN body responsible for vehicle regulation is preparing to impose its own data requirements on motor manufacturers from 2019, which insurers in the UK are hoping to influence for the benefit of motorists.
Experts have warned that the issue of who is responsible for a crash involving a driverless car could cause problems when motorists try to make a claim.
“Peter Shaw, Chief Executive of Thatcham Research, an automotive research centre funded by the insurance industry said: “One of the key battlegrounds of the future will be determining where liability rests in the event of an accident with an automated car.
“Future legislation needs to protect the consumer so that in the event of an accident, responsibility for the accident and who pays can be quickly determined.
“Was it driver error or a failure of the automated driving system? This can only happen if their insurer has access to key data about the crash. We are calling on car manufacturers and legislators to work with the insurance industry to develop a framework to make this happen.”
Earlier this year Transport Secretary Patrick McLoughlin said he believes the Government's proposed Modern Transport Bill will soon make autonomous driving a realistic prospect for motorists.
However, the first known fatality involving a self-driving car - involving a Tesla car on autopilot mode - occurred in Florida in May, and made some question the safety of driverless cars.
RAC head of external affairs Pete Williams said: "Considerable steps still need to be taken to convince the UK population of the benefits driverless cars will bring. There also remain significant legal, moral and safety considerations to be addressed before they become a common sight on our streets."