NAB, which owns Yorkshire Bank and Clydesdale Bank, had been lining up to acquire the assets from ABN Amro, the Dutch bank bought by RBS last year.

But yesterday, little more than a week after announcing its interest in the Australian and New Zealand operations, NAB withdrew from the sale. The assets are believed to be worth around A$800m, or £390m.

RBS is seeking to repair its tattered balance sheet by selling off non-core assets. Last month it completed a £12bn rights issue, the biggest capital-raising scheme of its kind in European corporate history.

Earlier this month Zurich Financial Services walked away from an auction to buy RBS's insurance division. The division includes Direct Line, Churchill, Privilege and Green Flag. Privilege and the motor business Green Flag have a strong insurance presence in Yorkshire and employ more than 3,000 people in Leeds, Sheffield, Doncaster and Pudsey.

RBS insists there is still interest in its insurance arm, which RBS is believed to be asking £7bn-£7.5bn for. However, some analysts believe the division may only fetch around £5bn-£5.5bn.

Two other bidders are reported to be in the running for the Australian unit – the Commonwealth Bank of Australia and Japan's Nomura. The Australian and New Zealand units comprise wholesale corporate and investment banking operations and two retail distribution joint ventures. It had about 750 staff at the end of 2007.

RBS is trying to repair its balance sheet which has been hit by writedowns from the credit crunch, and the takeover of ABN Amro for £50bn last year.

NAB did not give any reason for withdrawing from the sale.

In a brief statement, NAB said: "NAB previously announced it was participating in a process being conducted by the RBS to acquire ABN Amro Australian Holdings. NAB has now withdrawn from that sale process."