Charles and Patricia Lester said Lloyds criticised their business and breached client confidentiality when a bank official spoke about them on a radio programme.
The Lesters said they were being forced to accept life and pension cover through the bank as part of the refinancing. They recorded their bank manager telling them to agree the package or to take their account elsewhere.
The matter comes at a sensitive time for banks, which are trying to win back confidence after an avalanche of criticism from commercial customers.
Lloyds said it spent months sorting out the Lesters' finances and went on the radio to defend itself against 'unfair' comments from a client it said it had tried to help.
The Lesters, whose factory is based at Abergavenny in Wales, make expensive evening gowns. Clients include Barbra Streisand and Princess Michael of Kent.
Rising interest rates were straining the business, and the Lesters agreed to refinance. But they objected when the bank told them they must buy life and pension cover through Lloyds Bank Insurance Services. Mr Lester claimed the package would have cost pounds 5,000 more a year than he was repaying on existing borrowings, and he had wanted to arrange his own cheaper policies.
But in the recording, the Lloyds manager said: 'It isn't easy these days to get pounds 200,000 you know. If it's not going to be done as a proper package through LBIS, well I think that you've got to arrange through your agent to take everything, even the company account as well.'
Mr Lester replied: 'You mean you want me to take the company account away from Lloyds?'
'Yes, we would prefer, Charles, because we have bent over backwards here to help you,' said the manager.
The Lesters originally accepted but then switched to Barclays.
In a BBC radio programme about the company, Lloyds further angered the Lesters by saying they had a history of 'undisciplined borrowing and poor trading'.
Mr Lester said last week: 'We did not give them permission to talk publicly about our finances.
'Not only was it a breach of confidentiality, it was also untrue and defamatory.
'We are exchanging solicitors' letters but that is getting us nowhere. So I am now taking advice about pursuing legal action for compensation.'
A Lloyds spokesman said: 'The bank was unhappy at the prospect of delay in refinancing and had reached the point where either refinancing went ahead or the Lesters would be invited to seek alternative banking arrangements. The Lesters chose to move their accounts. We respect confidentiality, but we had a right to defend ourselves against what the Lesters were saying on the radio.'