The Financial Exclusion Committee says banks are failing the customers who need them the most, leaving the poorest to rely on expensive products.
It adds that controls on "rent to own" products and other high cost credit deals must be introduced urgently.
Banks should be required to have a duty of care towards their customers.
The report highlights how regulation has been successful in battling abusive practices by payday loan companies.
The government asked regulators the Financial Conduct Authority to limit the interest rates they are able to charge.
It calls for similar restrictions to be applied to other forms of high cost credit, charges for unarranged overdrafts and "rent to own" products.
These are products that allow customers to buy items, such as televisions or mobile phones, through rental deals which can cost as much as four or five times the normal price tag.
Debt charities say that as high cost loan companies have been pushed out, demand for credit by people in poverty has moved into other areas.
The government is urged to appoint a minister for financial inclusion who has to report annually to Parliament on progress made towards addressing financial exclusion.
Committee chair Baroness Tyler of Enfield said: "Too many people still have no bank account or cannot get access to basic or fairly priced financial services.
"The 'poverty premium' - where the poor pay more for a range of services from heating their home to accessing credit - contributes to a vicious circle driving people ever deeper into debt and distress."
She added that the victims of financial exclusion were "often the most vulnerable in society - the elderly, the poor or those living with physical disabilities or mental health issues".
"Action must be taken to ensure the financial system in this country works for all.
All too often, disabled customers are being failed by banks who are not adjusting their communications and procedures to serve them properly, she said.
The committee had been told of banks contacting deaf people by phone and sending written PIN numbers to blind people instead of using Braille, she added.
The British Bankers Association said it was already working closely with the government, the regulator and consumer advocates on a number of the areas highlighted in the report.
"We will consider the report's recommendations in detail and reflect on how they might be adopted by the industry going forward," it added.
Polly Mackenzie, director of the Money and Mental Health Policy Institute, said: "For too long it's been assumed that when people with mental health problems get behind on bills, or struggle to stick to their budget, it's because they're lazy or incompetent.
"That's simply not true, and we are delighted to see the Lords committee recognise this and the need for banks to step up and offer support.
"It's time for banks to adapt their services to help support people when they're unwell."
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