The Royal Bank of Scotland (RBS) saw its share price fall after the departure of Stephen Hester.
There is speculation that there has been some political interference in the move, which has resulted in RBS shares closing down 3.3 per cent in London, having fallen 7.5 per cent in early trading.
David Cameron's official spokesman said there had been no interference from the government in Mr Hester's departure.
RBS is currently majority owned by the UK taxpayer and is implementing several measures in order to recoup the money and return to the private sector.
One of these initiatives is to sell of branches and this is still ongoing. It will also reduce the number of staff by a further 2,000 in the next 18 months, which would take the total number of job cuts to 41,000 since 2008.
Lloyds Banking Group, which is also partially owned by the state, is implementing similar measures in order to return to the private sector.
By Tony Aynsley