Lloyds TSB is bidding for Britain's 2 million Muslims by making sharia-compliant current accounts and mortgages available from any branch nationwide.
Today's announcement came the day after Gordon Brown addressed the Islamic finance and trade conference to promote Britain as a centre for Islamic finance.
The chancellor said that British banks were "pioneering" Islamic banking. "London now has more banks supplying services under Islamic principles than any other Western financial centre," Mr Brown said.
Lloyds has also announced plans to launch other Islamic financial products later in the year, including an Islamic student bank account.
Under sharia law, the payment and receipt of interest is forbidden, making it difficult for Muslims wanting to borrow or save to access traditional banking services.
This has left many forced to choose between not using UK financial services or compromising their principles by using interest-paying accounts.
The current account being offered by Lloyds offers no credit interest and no overdraft facility.
Any funds held by the bank will also comply with Islamic law by not being invested in industries that are not permitted by Islam.
Under the terms of the Islamic mortgage, Lloyds will buy the property on behalf of the customers, providing up to 90% of the purchase price, with the customer paying 10%.
The customer will then pay the outstanding sum over an agreed term until they own the property outright, paying a rental payment each month in the meantime.
The bank said it had consulted with a board of renowned Islamic scholars to ensure that its products adhered to sharia law.
Paul Sherrin, head of Islamic financial services at Lloyds TSB, said its research found that more than 75% of British Muslims wanted current accounts and mortgages that fitted with their faith.
"By making these products available nationwide, we are bringing Islamic banking into the mainstream and we are giving the Muslim community access to financial services that meet their needs without compromising their religion," he said.
Meanwhile, the Islamic Bank of Britain last week launched a home finance plan that will allow Muslims to buy property together with the bank.
Similar to the Lloyd's home loan, homebuyers will pay monthly rent payments along with a monthly payment towards buying out the bank's share of the property.
Homeowners will need a 10% deposit and the maximum term is 25 years. During the term of the agreement, the property is held in the bank's name and the homebuyer holds a beneficial interest.
Ashraf Piranie, finance director at the bank, said: "Getting a foot on the property ladder has been a real struggle for many people, but for the Muslim community the problem has been compounded by the lack of sharia-compliant mortgage products."
He said he hoped the plan would offer Muslims a "real choice in line with their religious principles".