James Dalton, Association of British Insurers (ABI) head of motor insurance, said: "A car is potentially a lethal weapon."
He added that "radical action" is needed to "reduce the tragic waste of young lives on our roads, especially among the 17-24 age group".
An ABI spokesman told The Daily Telegraph: "Any restrictions to limit the number of passengers young newly qualified young drivers can carry for an initial period after passing their test would be a step in the right direction."
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Downpours keeping us on our toes today
The M20 in Kent has been closed in both directions after a pedestrian bridge allegedly collapsed on the motorway on Saturday.
The AA have warned of traffic jams and urged people to carry extra water in their vehicles because of the warm weather.