Nicholas Wilson claims that Dixons refuses to refund him the money he paid for the machine or offer him a new one.
The company insists on repairing it under the terms of its three-year warranty, which costs him an extra pounds 120.
Mr Wilson said Dixons even asked him to pay for the repair work first and said it would refund his costs.
The company only relented after he told it he did not have the money to do that.
Shortly after the first set of repairs, costing about pounds 300, the machine failed to work properly again.
Mr Wilson, who is also a part-time lawyer, said: 'I have reached the end of my tether. I compose film scores and the fax is crucial to my work.
'It seems to me that if the machine fails twice in a few months, as it has, then Dixons has sold me something that is not of merchantable quality, under the Sale of Goods Act.
'I must be entitled to a refund, not another repair which will probably fail within a few more months.'
Mr Wilson, who lives in north London, bought his fax, complete with answer machine and photocopier, at one of the company's Oxford Street shops in March 1992.
In addition to the cost of the machine, he took out a three-year warranty, priced at pounds 120.
'The salesman said that it would be worthwhile, because if anything went wrong with it, it might cost far more than that to repair the thing,' Mr Wilson said.
'In the summer of last year, the machine started to go wrong. Friends told me that they had put messages on the answer machine and I had not received them. Finally, I phoned Dixons in late October.'
The first repair firm Dixons told him to contact had gone bust months earlier. The second sent an engineer who informed Mr Wilson that the main circuit board, costing more than pounds 300, would have to be replaced.
'I received a letter from Dixons telling me that the quote I had received for the repair was acceptable and that I should pay it and send in the bill to them.
'I told them I could not afford this and they then said it would be OK for the company to invoice them directly.'
Within a few weeks of the repair, the machine began to fail in almost the same way.
In addition, its photocopying facility also broke down.
'The engineer came back and told me that the main circuit board needed replacing again.
'There is clearly a fundamental fault with the machine. What I do not understand is why Dixons won't refund my money or give me a new machine,' Mr Wilson said.
A report earlier this month by William de Broe, a London broker, suggested that up to 75 per cent of Dixon's pounds 77m pre-tax profits last year came from the sale of warranties.
The company has denied this but declined to give its own figures.
Fears that warranties represent poor value compared with extended manufacturers' guarantees prompted the Office of Fair Trading to announce an inquiry into their sale last month. Mr Wilson has sent details of his difficulties to the OFT.
A Dixons spokeswoman said: 'It appears there are a number of differences between Mr Wilson's account of what has happened and ours.'
Under the terms of the warranty, Mr Wilson is entitled to have his fax fixed.
But the company does not have to refund his money or offer a replacement until it becomes uneconomical for Dixons to repair it.
The company was now waiting for a further report before deciding whether to make such an offer to Mr Wilson.
She added: 'The normal system for repairs is that we operate a cashless repair operation.
'We do not expect a customer to pay out first, particularly for hefty amounts.
'Nor do we accept that the fax was not merchantable under the Sale of Goods Act. It did work well for 20 months after it was bought.'
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