Business secretary Vince Cable is sticking by his idea to break up RBS and make part of it a "business bank" which would focus more heavily on lending to small companies.

In a speech before the Lord Mayor of London at Mansion House, Cable expands on the idea - privately floated to David Cameron and Nick Clegg and leaked on Tuesday.

He says: "There has been a lot of interest in an option I floated in a private letter to the PM and DPM about creating a British Business Bank out of RBS.

"Indeed a lot of businesses I speak to have been supportive of such an idea but this would not be straightforward. It would almost certainly be necessary to lengthen the period in public ownership.

"It may well mean state-controlled banks being able to lend at cheaper rates than new commercial banks, thereby affecting the development of more diverse finance. And even if they did these things, we would run into problems with EU state aid clearance."

Although Cable explains the obstacles to his plan, he by no means rules it out. The except from his speech - which appears to have been included in the text at the last minute - comes as he talks of a "cleavage between the financial sector and other businesses," which is acting as a drag on the UK's growth prospects.

Cable argues that while lending has increased, the costs and conditions of that lending often make it unattractive to small businesses, saying:

We have a financial services industry in London that plays in the Champions League, with overseas owners to match, and a British business finance system which struggles in the second division.

"We have some of the world’s smartest, most creative, financiers, doing brilliantly in the City or Canary Wharf while there are also smart creative British entrepreneurs – or even run-of-the-mill smaller businesses – still struggling to raise finance to operate and expand.

"They depend, as one put it to me the other day, on the three ‘Fs’: friends, family and fools - shunned by banks, unable to access equity markets."

Cable's position on RBS presents a clear fault line between the Lib Dem minister and David Cameron, who has stressed that the coalition's aim is to return RBS to profit as quickly as possible and then sell it.

The idea is also opposed by Scottish First Minister Alex Salmond, who said it would lead to thousands of job losses at the firm's offices in Edinburgh.