A new High Street bank account compatible with Islamic sharia law is due to be introduced.
The bank has taken advice from Islamic scholars
The Lloyds TSB account will offer no interest or overdraft facilities, as under Islamic law the receipt and payment of interest is forbidden.
The introduction of the account follows the opening of a specialist Islamic bank in the UK last year.
Gordon Rankin of Lloyds TSB said its new account would make Islamic banking "mainstream".
"Our research shows that over three-quarters of British Muslims want banking services that fit with their faith.
"However, until now their banking needs have been largely uncatered for and many British Muslims have often had to bank in a way that is against their principles," Mr Rankin said.
Ibrahim Mogra, the chairman of the Muslim Council of Britain's Mosque and Community Affairs committee, agreed that many of the UK's two million Muslims have had little choice but to use interest-paying accounts.
"What the sharia scholars tell us to do is whatever interest you gain you get rid of it without the intention of gaining reward from God.
"Even though at the end of the year I just take the interest out and give it away, I've still, in a way, handled money from interest which I really shouldn't be doing," he said.
Until the opening last year of the first UK-based specialist financial institution - the Islamic Bank - Muslims were able to access sharia-compliant current account facilities only through Middle Eastern banks with branches in the UK.
The Islamic Bank opens its third branch in Leicester on Tuesday and plans to open five more by the end of 2005.
Ibrahim Mogra of the MCB believes other high street banks will now follow Lloyd's TSB's lead:
He said: "The high street banks want to hang on to their customers and now there is an Islamic bank available they may be anxious they might lose their customers.
"I think all High Street banks will take this route sooner or later because there's a huge Muslim market in the UK."