The survey singles out National Westminster as the worst for dealing with standing orders and sorting out mistakes.
Other banks receiving some praise for their current account service are the Co-op and Bank of Scotland, despite lukewarm levels of overall satisfaction in both cases.
Barclays, TSB, Clydesdale, Royal Bank of Scotland, and the Halifax and Nationwide building societies are all described as 'average' for overall satisfaction. Lloyds and Midland Bank are rated as below average overall, while Midland shares joint worst place with NatWest in terms of its efficiency.
The Which? survey polled 7,000 of its readers at random this summer, of whom just over half replied. While the survey was not based on weighted averages, the magazine claims to have obtained a good response from readers across all banks.
It found that one in five readers had problems with a direct debit or standing order in the previous year.
One in seven respondents had an incorrect amount taken out of their account, while one in eight were wrongly charged.
The magazine concludes: 'These figures make a mockery of the Code of Banking Practice, introduced in March 1992 to improve customer satisfaction. More than one in 10 people who replied are still not satisfied with their current account, no different from our survey last year.'
Which? blames the problem partly on poor communication from banks and building societies to their customers. Its survey shows one in five people are unhappy with advice on charges and a quarter with information on interest rates.
A NatWest spokesman said: 'We are naturally disappointed that the survey identifies us, particularly as we have done so much to improve our service. This includes extended Saturday opening, including counter service. In March this year, we introduced a system of pre-notification of charges.'
He added that NatWest's complaints in the first nine months of this year are 12 per cent down on the same period in 1992. NatWest's own quarterly survey, which produces responses from 100,000 customers, shows a satisfaction rating of more than 90 per cent.
An Abbey National spokesman said: 'We are very pleased with the results. They show that we give good service to our customers and resolve things in the few cases when we get them wrong.'
Customers who are unhappy with the service they receive are advised by the magazine initially to contact their branch, setting out their complaint in writing. Copies should be kept of all correspondence.
Claims should also be made for out-of-pocket expenses, such as telephone calls, as well as for the time spent writing letters to sort out the problem. Which? recommends claiming the bank's own going rate for a letter, usually pounds 10 to pounds 15.
If the matter is not resolved within a satisfactory time, customers should write to the bank's head office, before taking the matter up with the Banking or Building Societies Ombudsman. Complaints usually have to be taken through a bank's internal system before they can be dealt with by an ombudsman.
In his annual report, the Banking Ombudsman, Laurence Shurman, last month admitted that some banks take too long to resolve complaints, while many local branches still do not display posters advertising his office's services in a prominent position.
His office has introduced a system whereby if it believes a complaint is one that can be taken up, the bank will be informed and expected to sort the matter out within six weeks. This in effect puts in place a two-tier complaints system where customers feel their bank may be dragging its heels.
But Mr Shurman ruled out compelling banks to publish figures for the time it takes them to resolve complaints from the public, claiming his job was not to regulate their behaviour.
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