But as several building societies have followed Abbey and lowered their charges, there are signs that it may signal a price war involving the entire banking sector.
So far the banks are standing aloof, refusing to join the scramble to cut their rates, which stand at a minimum of 18 per cent APR, plus additional monthly charges of between pounds 8 and pounds 10.
Building societies have been swifter to move. Earlier this week, Nationwide - Britain's second-largest society - decided that from 1 August it will charge its 1.2 million FlexAccount customers 11.5 per cent APR for pre-arranged overdrafts, down from 18.1 per cent. For those who also have a mortgage with Nationwide, the rate will drop to 8.74 per cent.
And last week, the third-largest society, Woolwich, announced that it would cut overdraft rates for its 365,000 current account holders from 19 per cent APR to 9.8 per cent.
These moves came on top of what proved to have been the opening salvo in this war, fired in May, when Halifax cut rates for its 750,000 Maxim cheque-account holders to 12.4 per cent.
Other building societies have already signalled that they may be prepared to follow suit.
Alliance & Leicester, the fourth-biggest society, which launched a new account two weeks ago, looks set to join the bandwagon within days. 'We are actively considering a reduction in our authorised interest rates in the next few days which we believe will be very competitive,' a spokesman said.
Compared with the banks' grip on the current account market, however, building societies are small beer. More than 30 million current accounts are held at the five main UK banks - National Westminster, Barclays, Lloyds, Midland and TSB. For the banks, therefore, an all-out price war would be a very serious affair.
But for the building societies the logic is simple. By cutting rates they hope to build market share in an area in which they are barely represented. Moreover, loss-leading current accounts can generate more profitable business.
John Aitken, a senior banking analyst at UBS, the brokers, explained: 'First, when people move their accounts they are bringing over their deposits. Deposits can act as the seedcorn building societies need to carry out their traditional lending operation.
'Secondly, and probably more importantly, if you have a good relationship with your database, it will tell you how much a person earns, how much they pay into their account, what their standing orders are, what life insurance cover they have and so on.
'Having that information is a crucial part of the process involved in selling more products.'
The result has been that even as base rates have dropped, overdrafts have remained costly.
The banks defend overdraft rates by reference to how much it costs to run a current account.
Barclays was unable to say what it costs to service an overdrawn account, including bad debts. But industry estimates suggest interest rates would need to be at least 15 per cent to do so.
The rest - plus charges - is profit, until now used to cross- subsidise other areas of the bank's operations and adding to its bottom line. Which is why a price war would be so painful for the banks.
Their traditional dominance in current accounts have left them with sizeable overdraft books. Barclays' customers owe it pounds 800m, while NatWest's are overdrawn to the tune of pounds 1bn. Lloyds' overdraft book is believed to be about pounds 1.5bn. Midland Bank's overdrafts are thought to be pounds 500m, with those of Royal Bank of Scotland totalling pounds 325m.
Between 20 and 30 per cent of the big banks' customers go overdrawn by agreement in any year. By comparison, only 60,000 of the 1.5 million customers of Abbey National - now a bank but until recently a building society - go overdrawn by agreement, owing an average of pounds 200 to pounds 300.
Nevertheless some commentators, such as John Aitken, believe the building societies' rate cut is more of a headline-grabbing exercise than one aimed at winning thousands of former bank customers.
'You have to remember that for the most part they do not want all the banks' bad debts. But if they can add a few thousand accounts they will be quite happy,' he said.
A few thousand lost accounts would hurt - but not enough to persuade the banks to go to war, given the risks, he said.
Nevertheless, he said: 'All the banks are monitoring the effect of these cuts on a daily basis. If they felt that they were losing too many customers they would have two options.
'One would be to cut their own rates. You have to remember that for most of them, overdrafts are a minuscule amount of total business, 1 per cent or so.
'The second option would be to extend the attack into other areas of retail business, such as mortgages. They could, for instance, offer home loans at cost or marginally above, really eating into the building society market.'
In any event, banks will continue to hold on to the lion's share of the market, if only because of their high name recognition. 'Let's face it, if you are on holiday in the Scottish Highlands and you try to pay your hotel bill with a building society cheque, someone is going to look at you a bit oddly, even nowadays.'
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