Money Box listeners say basic bank accounts are too limited for modern day needs.
Since 2004 banks are committed to offering basic bank account for people who want to ensure that they do not overdraw their account.
But 6 out of 17 basic bank accounts surveyed do not provide a debit card, according to latest figures from the Financial Services Authority.
Debit cards allow customers to pay for goods electronically in shops and online.
This lack of access to basic banking services is being blamed for the rising number of people who have benefits loaded directly onto pre-paid cards.
Although charges vary, many card companies charge to have benefits paid onto cards, to take out cash, and often a regular fee as well.
But Money Box listener Gordon Wilson from Glasgow, says he has been refused a basic account by RBS, Natwest and Bank of Scotland on the basis of his credit record even though he is not seeking credit, and has not been declared bankrupt.
Francis from Liverpool says his basic account does not allow him to pay direct debits; he uses a pre-paid card to pay utility bills.
Presenter Paul Lewis puts the issues to the Government's lead on Financial Inclusion: Exchequer Secretary to HM Treasury, Sarah Macarthy-Fry.
This item was first broadcast on Radio 4's Money Box on Saturday, 30 January 2010