The best chance you have is to kick up a stink with the solicitor who assisted in the purchase of your house.
One of the standard enquiry questions that a buyer's solicitor asks the seller is something like 'what remedial work covered by guarantees exist in relation to the property and please provide the certificates. This should have elucidated the damp-proofing, and the solicitor gets the certificates. He should then have passed them onto you on completion, having checked that the warranty is transferable (or advised you accordingly if it wasn't).
I suggest that you write to this solicitor outlining the problem and asking for his comments in relation to the assertion by the damp company. You don't have to employ a solicitor to pursue a complaint against another one - and at this stage I suggest you don't call it a 'complaint' - just ask for their comments - then decide what to do. Solicitors have to have professional indemnity insurance to operate as a practice, so they won't take it personally. Would you would then do, assuming the answer isn't satisfactory in excusing them, is to make a complaint against the Practice via the Senior Practice Manager. The objection is to get their PII to pay for the remedial work, plus the cost of a new insurance policy at their expense for the remainder of the warranty period.
These people are paid well enough - they need to perform or suffer the consequences.