Best I can find is this, from:
BA World Cargo - Products and Services - Products
- apologies if you've already seen it:
On arriving into London
........collect your pet from the Animal Reception Centre. These can be found:
At Heathrow Airport - Animal Reception Centre, Beacon Road, London Heathrow Airport, Hounslow, Middlesex, TW6 3JF (Beacon Road is located off Sanctuary Road on the Southern Airport Perimeter Road).
c/o James Cargo Services Livestock +44 (0) 1753 682244
At Gatwick - Animal Reception Centre, Cargo Forecourt Road, Gatwick Airport, West Sussex, RH6 0SQ (located off the Airport Perimeter Road North and Cargo Road).
c/o Animal Aircare +44 (0) 1293 555580
The clearance time for pets from EU countries will be completed about 2 hours after your time of arrival but will take longer for pets arriving from non-EU countries due to additional HM Customs clearances.