Using the FTA verification tool
The FTA site lists TRN/TIN verification among its other links. It opens a form with separate fields for a TRN and a TIN, each protected by a captcha code. Enter the number exactly as printed, complete the captcha and submit; the result tells you whether the number is registered and the name it belongs to.
Check the returned name against the supplier's trade licence. A valid TRN belonging to a different company is as much a problem as an invalid one.