The investigation follows an uproar among customers of Northern Rock, the former building society which became a bank last autumn.
Helen Liddell, the Economic Secretary to the Treasury, said: "I am extremely concerned about evidence of banks not being straightforward in their dealing with their customers - in particular, not alerting customers that they could get a better deal with a different account. I have asked my officials to investigate urgently."
Mrs Liddell said she would speak shortly to the banks with a view to toughening the Banking Code. "I am keen to ensure that consumers have confidence based on clear and accessible information in the banks and building societies they do business with."
In the last week of April, thousands of savers with Northern Rock were switched between bank accounts without being consulted. Eleven kinds of bank account were merged into three. In many cases, interest rates were lowered.
Northern Rock justified its decision on the basis that there would be as many gainers as losers from the changes.
Yesterday, Mrs Liddell met David Davis MP, chairman of the Public Accounts Committee, who brought the behaviour of Northern Rock to her attention. Mr Davis complained that people had not been told of interest rates going down.
Such is the anger over Northern Rock's decision that its switchboards have been continually jammed by savers querying the changes. The Office of Fair Trading and the Banking Ombudsman have received complaints and are considering whether to take action.
Professor Roy Goode, a Northern Rock saver who also led the government inquiry into the Maxwell affair, has branded the move "unfair and improper".
Northern Rock has in the past said it is on the right side of the Banking Code, but was last night unavailable for comment.