PPL represents record labels and performers; PRS for Music represents songwriters and composers. Together, as PPL PRS Ltd, they sell TheMusicLicence — the combined licence most UK businesses need to play mainstream commercial music in public. Their letters, invoices, calls, and visits go to venues they believe are playing music: salons, barbershops, cafes, restaurants, shops, gyms, clinics, hotels.
The claim in the letter is a starting position, not proof. You are entitled to ask, in writing, which repertoire they believe you use and how any figure was calculated. What loses you ground is silence: ignored letters escalate to firmer letters, invoices, chasing calls, and eventually legal action. Respond in writing, keep records of exactly what you play, and choose one of the routes below.