Firstly, seek proper legal advice.
I will, however, offer my non-professional take on this situation.
Was this letter the first time that the company made you aware of the debt? If not have you ever agreed with them that the debt exists?
I ask this because the
Limitations Act 1980 allows creditors to commence action through the courts on an
acknowledged debt up to 6 years after the last contact made in which you agreed you owed them money. (I should add that the six year rule does not mean that a debt disappears after this time, only that it becomes unrecoverable through the courts.)
Read
here to get an idea of what they can do to reclaim their money.