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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England have been beaten by nine wickets against Pakistan in the first Test at Lord's.
Mayor of London Sadiq Khan is backing the scheme.
Sunday will be a fine day across much of Scotland and northern England, with much less coastal mist and low cloud than yesterday.