Vince Cable thinks there is a dearth of "compelling vision" by the government, according to a leaked private letter to the prime minister.

Cable, the business secretary, tells David Cameron that he also thinks the government lacks a "clear and confident message about how we will earn our living in future" in relation to business and industrial policy.

The letter, dated 8 February and revealed by BBC News, urges Cameron to be "more strategic" and "ambitious" in the future.

Cable also calls for the bank RBS, which is 80 percent owned by the taxpayer, to be broken up.

"My suggestion is that we recognise that RBS will not return to the market in its current shape and use its time as ward of state to carve out of it a British business bank with a clean balance sheet and a mandate to expand lending rapidly to sound business," he wrote.

He picks out the digital and creative industries as fertile ground with "huge potential", though he writes that "despite fantastic small and medium-sized enterprises, we have produced no Amazon, no Google, and no Intel."

As well as this he accuses the government of not showing enough leadership in "identifying and supporting key technologies" and describes the government's action in this area as "piecemeal".

Appearing on BBC Radio Four's Today show in the morning before the letter leak, Cable had said that the Liberal Democrats and Conservatives were negotiating over scrapping the 50p top tax rate.

"If [the 50p rate] were to go, it should be replaced by taxation of wealth, because the wealthy people in the country have got to pay their share, particularly at a time of economic difficulty," he said.

"How exactly that is configured is a detailed matter for negotiation. But that principle must be upheld, and a mansion tax actually is a very economically sensible way of doing it."