Mr Dobson ordered all NHS trusts to use their existing powers to charge insurance companies up to pounds 2,949 for in-patients and pounds 295 for out-patients for treatment after road traffic accidents.
Confirming a report in yesterday's Independent, Mr Dobson said the Government would introduce legislation when it had Parliamentary time to put the onus on insurers to make the payments.
The Government estimates the move could save the NHS pounds 100m but some insurers estimated it could raise the cost of an average annual premium by pounds 20 to pounds 370.
The NHS trusts will be asked to identify cases where they have treated traffic accident victims and where somebody else seems likely to have caused the accident; find out whether those patients are claiming compensation; discover who the insurers are; and lodge claims.
Mr Dobson told the trusts that they should pursue their claims "vigorously" and should not be put off by the paper chase, which had stopped many from using their powers.
To cut costs, the Government is also scrapping the pounds 21.30 charge which hospitals and GPs can claim from drivers who seek immediate attention.
The Department of Health said the collection of the fee put NHS staff in difficult and potentially violent confrontation with patients.