The Alliance & Leicester (A&L) bank has apologised for a letter sent to customers who are trying to reclaim overdraft charges.
The Alliance & Leicester says only a few letters were sent out
The letter cited last week's favourable court ruling for Lloyds TSB in which that bank won a judgement in Birmingham county court.
The A&L also hinted that it might have to close the account of one customer if he did not accept an offer of £66.
Such a move could be against industry rules about treating customers fairly.
The letter has been sent out to some customers by the A&L's legal firm, Wragge and Co.
In it, the bank's lawyers claim the Birmingham ruling in favour of Lloyds TSB was a precedent, although it also admitted that the ruling was not binding.
"It may be relevant to you....to consider also the decision which has recently been reached in Birmingham County Court on the first of the 'bank charges claims' to come before the court on an adjudicated basis.
"We are aware that the decision is not necessarily binding at first instance on other Judges in other courts around the country.
"That said, this case is a precedent and our client will rely upon it in the course of these proceedings."
One man who received the letter, John Smith from Leicester, said he thought it was an attempt to put him off pursuing his claim for £3,000.
Letter from lawyers for the Alliance & Leicester
"It's disgraceful," he said.
"They are trying to intimidate me no doubt," he added.
The letter he received referred to the possibility of his account being closed if he did not accept A&L's offer of a £66 settlement.
"We would like to reassure you that if you do accept our offer of settlement we will continue to operate your account," it said.
"We would only do so on the basis that you accept the terms and conditions of your account previously notified to you and that charges will be applied in accordance with our current charging policy."
In February, the Financial Ombudsman Service criticised the A&L for closing the accounts of some customers who were suing the group for excessive overdraft charges.
The bank was ordered to pay compensation to one man whose account it had closed, with the Ombudsman ruling that the customer had the right to complain about the charges without the threat of punitive action.
The letter has been received by other A&L customers who have also complained to the BBC News website.
When asked about these letters by the BBC, an Alliance & Leicester spokesman said it had only been sent out to a small number of customers.
"We apologise if any customers were concerned by the tone of the letter as that was not the intention.
"As soon as we became aware of this, we instructed them (Wragge and Co) to remove any reference to the (Birmingham) case," he said.