A group of influential MPs has accused banks of treating people on low incomes like "second class citizens".
MPs want banks to do more to encourage people to open accounts
The Treasury Select Committee estimates that eight million people are excluded from financial services.
Labour MP John McFall criticised banks for giving basic account applicants "short shrift" and urged them to do more to include low-income customers.
The banks say they have created millions more basic accounts and made it easier for people to use services.
In its report - Banking The Unbanked - the committee urged banks to get rid of "unreasonable" penalty charges and introduce a £10 penalty-free buffer zone to help those on low incomes to manage their finances.
But it did not go so far as to call for new legislation to force all banks to open their doors to basic bank account holders.
During the last three years, around 1.97 million basic bank accounts have been opened in the UK.
The accounts are designed to encourage people who would not qualify for a standard bank account to enter the banking system.
Basic account holders can use direct debit services as well as access ATMs. However, there are systems in place to prevent them getting overdrawn.
But a recent investigation found that some banks did not provide prospective customers with sufficient literature or advice, or made it difficult for them to open basic accounts at high street branches.
The treasury committee said progress had been made towards a target of halving the number of people who do not have access to a bank account.
But it urged banks to "redouble their efforts" to encourage more people to open accounts.
Mr McFall, committee chairman, said it was important to give low-income households access to financial services so they do not fall into a situation where they are at the mercy of loan sharks.
He said: "A basic bank account is often an essential stepping stone to full financial inclusion for many people in society.
"It helps them to gain legitimate employment, manage any debt they have and become accustomed to financial products."
But he added: "Some basic bank account applicants receive short shrift at bank branch counters.
"Treating basic bank account holders like second class citizens by denying access to branch counters causes exclusion and reduces the opportunities for holders to become further integrated with the financial services sector."
He called on the Banking Code Standards Board to take action against any financial institution which was discovered to be dissuading people from opening bank accounts.
A spokesman for the British Bankers' Association said bank customers were not regarded as second class citizens and its members were committed to doing more to encourage people to open accounts.
"There has been recognition that banks have done a great deal to get people into banking services," he said.
The report also found that the Post Office had "enormous potential" as a gateway to banking and financial services.
A government spokesman said it would be studying the findings, but added that "steady progress" had already been made to halve the number of people without access to a bank account.