The Association of British Insurers (AIB) has estimated that motorists could save £15 on their premiums thanks to the data being put online.
The savings would not be felt by motorists who had lied about their driving record.
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The PM faces a countdown to settle a deal before her minority government tries to get its Queen's Speech plans approved by the Commons.
More details will come today on proposals to offer EU residents the right to a new "settled status" in Britain after it leaves the bloc.
Scotland and Northern Ireland could see rain later but for the rest of the UK it should be a fine day.