Lloyds TSB lent a couple on benefits £20,000 even though they could not afford to repay the money, according to BBC documentary Real Story.
Lloyds TSB says it works closely with debt advice agencies
The programme says the group admitted its actions broke the Banking Code, the rules governing the behaviour of banks.
It is alleged the jobless pair were also sold an expensive loan insurance plan to protect jobs they did not have.
Lloyds TSB said the "historic case" was two years old, and that it remained a "responsible lender".
It said it later offered the couple a refund - "an offer made long before we were contacted by the BBC".
Real Story: Are banks taking advantage of their customers?
Monday, 19 July, 2004
19:30 BST on BBC One
The programme also alleges that the same branch in Burton-on-Trent encouraged a blind man to take out a loan, with a payment protection plan that ended up being worth nearly a fifth of the final loan.
He was unemployed at the time. Lloyds TSB later repaid £6,000 run up in payment protection insurance and
interest by the man.
Iain Macqueen-Sims, an independent consumer loans expert, told the programme: "You would expect this sort of behaviour from a cowboy, from a back street broker or a loan shark. One would not expect this from a major High Street bank."
The documentary says banking authorities are now deciding what action to take.
But the Banking Code Standards Board has denied that its regulations are not tough enough.
"We have strong sanctions - we can name and shame, and we can direct people to do things," the BCSB chief executive Seymour Fortescue told BBC Radio Five Live.
"The only thing we can't do is fine people, and the government report which looked at us in great detail said we were right not to seek the power to fine."
He said banks and building societies disliked being named and shamed, and that they "fight like mad to resist that".
A Lloyds TSB spokesman said: "The two customer cases mentioned in the Real Story (documentary) are historic cases relating to loans granted in 2002.
"In both cases we have worked with the Citizens Advice Bureau to review the circumstances and reach a settlement.
"In the case of (the couple) Mr & Mrs Davis, we acknowledged that while the consolidation loan helped them repay debts with other companies and reduce their monthly commitments, more could have been done to assess whether this reduced amount was affordable."
In this case, Lloyds "hadn't done everything we could have done under the Banking Code", the spokesman said.
"It is clearly not in our interest to lend money to people that cannot afford to repay it and we are committed to being a responsible lender and identifying and supporting customers in financial difficulty. "
Real Story is on BBC1 on Monday at 1930 BST.