Even the generic meet and greet companies which charge in the region of £150 or so per person to have someone meet you at the aircraft and help you expidite the arrival/transit process don't have a dedicated lane for the UK border at Heathrow so all they'll do is accompany you and stand in line at the relevant queue. The only service which has a dedicated UK Border is the Windsor Suite / Heathrow VIP that charges a four figure sum for the privilege.

Gatwick on the other hand will be making a Premium Passport lane available again for arriving passengers from June 2023 according to the airport website with prices starting at £10