I have recently received solicitor’s letter, on behalf of an

I have recently received solicitor’s letter, on behalf of an organisation called “British Oil Security Syndicate” falsely accusing me of fuel theft and requesting a balance to be paid. Initially I thought that this might be a scam letter, and still unsure.
I responded (by letter and email) to confirm that I did attend a filling station forecourt approximately 15-20 minutes prior to the alleged offence time, but solely for the purposes of making a CashPoint withdrawal. At the time of the alleged office I was at a nearby gym with a personal trainer who is happy to confirm the time period that I was with him.
In my response I also confirmed mobile ‘phone records would be able to pinpoint my whereabouts at the alleged offence time.
I also replied that there is no doubt that an error has occurred and that they should re-visit the accuser and check their records (presumably CCTV).
I have now received a final demand requesting payment within 7 days. As the demanded figure is small (less than £80) it is tempting to pay, however I know that this is might then incorrectly admit liability.
I have no issues in embarking on a full legal process to defend this accusation, but would appreciate your advice as to how I should move forward.