The deal is the latest attempt by one of the Big Four banks - which also include HSBC, Lloyds TSB and Royal Bank of Scotland-owned NatWest - to counter criticism of their current accounts. The four have been the target of a long-standing campaign by Which?, the consumer group, which has been urging customers to move to smaller banks or building societies.
Traditionally, the Big Four have paid almost no interest at all to customers in credit, while charging overdraft rates in excess of 15 per cent. However, last year Lloyds began offering credit interest of 3.93 per cent a year to customers paying in at least £1,000 a month. In addition, HSBC has launched a regular savings account offering 8 per cent annual interest.
Alliance & Leicester now offers its current account customers a regular savings deal paying 10 per cent, while Abbey is paying 6 per cent on current account balances for the next year.
A spokesman for Barclays said it would match the overdraft limits available to customers at their existing banks.
However, Andrew Haggers, of market analyst Moneyfacts, said: "While people are happy to switch credit card provider on a regular basis to chase introductory deals, they are less likely to change current accounts due to the perceived hassle."
Nationwide Building Society and the internet-based banks Cahoot and Smile currently top best-buy charts, paying interest on credit balances of at least 3 per cent a year while offering overdraft rates below 10 per cent.