RBS pledges Hester will stay to 2014

The news emerges as Mr Hester comes under pressure as bankers are set to be paid £250m in bonuses despite a likely £500m fine for the group's role in the in the Libor-rate rigging scandal.

Shareholders had already been concerned that Mr Hester could leave RBS before the sale of the taxpayer's 82 per cent stake in the bank, following the public furore over a £1m bonus last year.

Mr Hester was badly hurt by the criticism, claiming to have come "within inches of quitting", and told staff that the attention made the job of reviving the bank "harder".

He eventually declined the near-£1m pay-out – an amount London Mayor Boris Johnson attacked as "absolutely bewildering" – even though the board felt that he had earned the money by making the bank a safer institution in which to invest.

The RBS boss is considered by many investors to be the main force behind the bank's turnaround in fortunes. At the current trajectory of RBS's share-price recovery, the Government could break even, or even make a profit, if it sold the bail-out shares in the next 18 months.

A leading RBS investor said that Sir Philip recently insisted that Mr Hester will be around until the middle of next year, which should allow him enough time to oversee a settled sale of the Government's huge RBS stake.

This could also be the ideal timeframe for the former Financial Services Authority boss, Sir Hector Sants, to take over at RBS, a rumour that swept the City recently. Sir Hector is currently easing his way back into the private sector with a head of compliance and regulatory relations role at Barclays.

A second shareholder said that the comments came as a relief.

He added: "When there was all the outcry [over the bonus], we were saying 'No! We need him'. OK, the money was a lot in the real world, but it is low for the job he's doing and the Government will know that Barack Obama got political capital out of making a profit from selling stakes in the banks."

Mr Hester said he would wave his 2012 bonus in the wake of a technical glitch at RBS's NatWest subsidiary in June that left customers unable to withdraw cash. However, he is still eligible for millions of pounds in deferred bonuses.