Banks are being criticised for failing to cater for the poor and leaving them at the mercy of loan sharks.
The New Economics Foundation (NEF) said big banks were cherry picking customers for premium accounts.
It is calling on the government to force banks to make basic accounts available to everyone who wants one.
A spokesman for HSBC - expected to announce record profits on Monday - said UK customers enjoyed free banking when their accounts were in credit.
The bank also said that Britain only accounted for 20% of its total profits.
The NEF said the ability to open a bank account was fundamental to being able to participate in modern economic life, enabling people to take advantage of the discounts available for paying for things by direct debit.
Obligation
The group said about 11% of adults in the UK do not have access to a bank account, rising to 35% in poorer areas.
It is calling for the introduction of a Universal Service Obligation for banks similar to the one that applies to utility companies.
Whitni Thomas, head of access to finance at the NEF, said: "The banks are cherry picking the most profitable customers - only paying lip service to tackling financial exclusion.
"Their lack of action leaves the most vulnerable marginalised from mainstream financial services"
"Their lack of action leaves the most vulnerable marginalised from mainstream financial services, paying more for everyday goods and with no option but loan sharks for credit.
"A Universal Service Obligation would guarantee the right to a transactional bank account for the UK's poorest consumers.
"It should be a simple quid pro quo for the licence to operate in a lucrative and well protected market."
The NEF said in 2004 the four largest banks collectively made profits of more than £23bn, or about £26 per customer.
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