The proposals under study by the DoT include the privatisation of the Driver and Vehicle Licencing Agency so that insurance records can be kept against its vehicle registration database.
Heavier fines and stiff compensation orders for uninsured drivers who have caused damage or injury to other people are also being called for in the plans being put forward by the Motor Insurers' Bureau.
The MIB is the body set up by the insurance industry to pay claims made by victims of uninsured drivers. Last year, the total number of claims stood at around 40,000 - almost 400 per cent up on 1988.
The MIB estimates that about one million motorists are uninsured in any one year. Compensating the victims of untraced or uninsured drivers costs insurers about pounds 250m per annum.
While policyholders pay the cost in terms of higher premiums, victims pay the price in other ways. Last year, more than 5,000 people received compensation from the MIB for personal injuries.
Roger Snook, claims manager at MIB, said: 'The evidence is that this is a growing phenomenon, which society as a whole has to pay for at the moment.
'What we are suggesting is that the matter could be addressed by vigorously enforcing the rules. This would include checking that people have paid car tax, which is linked to paying insurance.
'Motorists should also be required to carry their driving licence and insurance documents with them all the time. Insurance certificates should be standardised, and the information collected by police when they attend an accident should be, too.'
Mr Snooks said that magistrates should be given the power to make compensation orders to the MIB: 'At the moment, they are empowered to direct money to the BBC in the event of people not paying their television licence fees.
'I would argue that compensating people who have been injured is probably higher up the list of priorities than that.'
He accepted that the cost of recording insurance details on the DVLA's database could prove expensive: 'That is why the industry would be prepared to consider running DVLA as a privatised entity if necessary,' he said.
'Some people would argue that it is the recession that has caused a minority not to take out insurance. But they are still well-off enough to run cars. They should be told that their cars will be impounded unless they pay the insurance or a fine. If they don't do that within a given period, the car could be sold off to cover the cost.'
Mr Snooks said it was too early to say whether the proposals would receive the DoT's support. However, he and others in the insurance industry who had drawn them up were hopeful that at least some of them could be implemented quite rapidly.
A DoT spokesman said: 'Our primary concerns are twofold. Firstly, we are concerned at the possibility of potential or real injuries to innocent people.
'Secondly, there is the concern that if people are not paying insurance, they are also not paying their car tax and therefore forcing other people to bear extra costs.
'There is no doubt that we are looking very seriously at these proposals. If any do appear to us to be sensible then we would want to see whether they are practicable.'