AA Insurance warned that around one in 25 drivers in this country has no insurance, meaning the chances of being hit by one are greater than almost anywhere else in Europe.
New rules which came into force today, raising the fixed penalty for driving without insurance from £200 to £300, will not deter offenders who often have a string of previous driving convictions, it said.
Uninsured drivers kill more than 100 people every year and injure around 23,000. AA Insurance said law-abiding drivers are angry at what they see as "light touch" penalties and 81% of nearly 20,000 AA members want to see a stronger clampdown.
Offenders are often young men, but the typical cost of car insurance for a man aged between 17 and 22 with a clean licence is four times the size of the new fixed penalty at £1,211.
More than half (54%) of people think uninsured drivers should face jail and two-thirds (63%) want to see them electronically tagged, the research found.
Eleven thousand uninsured drivers who were convicted last year had already been banned from driving.
Mr Douglas said: "These are typically young men in cars that may have no MOT or tax. Offenders often have no driving licence or are already disqualified."
He said many offenders often go on to "obtain another cheap banger for cash, no questions asked", and carry on breaking the law.
Fixed penalties generally cover more minor motoring offences and serious offenders are likely to end up in court, where the maximum fine is £5,000.
But fines are means-tested, meaning that the average court fine is less than the new fixed penalty at £299.
Innocent victims who have been hit by uninsured drivers often lose their excess and no-claims bonus because they have no insurance company to claim against.
But they can make a claim through the Motor Insurers' Bureau (MIB), which is funded by the UK insurance industry - and ultimately the premiums of well-behaved motorists.
This safety net for insured drivers means they can claw their lost no claims discount back, but this tends to take several months due to the legal processes.
Mr Douglas said: "Uninsured drivers cost this country at least £380 million every year and add about £33 to the cost of every car insurance policy, quite apart from emergency services and court costs."
He called for a "tough, no compromise approach to uninsured drivers".
Police were given more powers to stop vehicles identified as being driven without insurance eight years ago. Since then, 500 vehicles have typically been seized each day, of which around a third are crushed.
But AA Insurance has pointed out that there are still around a million vehicles on Britain's roads being driven without cover, equating to one in 25 drivers.
It contrasted this estimate to MIB figures showing that only around one in 500 drivers in Germany are uninsured, while in Sweden the figure is put at one in 1,000.
Equipping more police cars and fixed points such as garages with automatic number plate recognition (ANPR) technology would see more uninsured drivers being stopped quickly, it said.