City law firm Taylor Wessing is believed to be working on a plan to create a bank backed by six leading UK listed corporates disenchanted with the failing lending institutions in the Square Mile.

The firms are thought to have sounded out Glenn Cooper, the banking veteran famed for floating Manchester United, to head the new bank.

A City source said: "These guys are totally fed up with the problems with the inertia, so are looking to get together and create an institution that can lend to small and medium-sized firms. Given that most banks have horribly messy balance sheets, they figure it's easier to start from scratch."

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The group of firms, which is thought to include one FTSE 250 company, is believed to have begun working on the plan late last year. The bank would look to use wholesale funding lines, guaranteed by government, that would lend to firms. Tentative approaches to government officials are thought to have been made.

Mr Cooper, who is currently working on raising investment for a £500m activist fund targeting FTSE 100 companies such as GlaxoSmithKline, was a director of City merchant bank, Ansbacher Holdings during the 1980s and 1990s. In 2007 he spearheaded a campaign against Vodafone and its chief executive, Arun Sarin, calling for the sale of the company's stake in American group Verizon.

News of the initiative comes just days after Gordon Brown's announcement of a second government bank bailout failed to allay the fears of continuing banking failure in the City.

Barclays's chief executive John Varley sought to calm the bank's investors on Friday saying he would prefer to pay for state insurance on assets with cash rather than giving up equity. The bank had sold sufficient amounts of assets last year to enable the it to avoid dipping into the Government's bailout fund, he said.