Can tell you one not to use, we have flown for Heathrow once, last Oct (06)
Parked with Purple parking, reserved elsewhere but they closed so PP took our booking.
It is a massive lot with 1000's of cars parked there. Got back after our 12 hour flight from LA, left us waiting for over 1 hour stood in the freezing cold while they came for us. Then asked us to stay on the minibus when everyone else got off, we knew something was wrong at this point but the driver did not know so 10 mins before we got to office to find out. They had our £30,000 4 month old BMW. DW was very tired and very mad at this point.
They eventually told us they had lost our keys, at least 3 other families in the office with lost keys, and damage to cars.
They brought us back upto Yorkshire in Minibus, took spare keys back down then drove our car home with another driver following. I suppose we could not fault them looking after us to get us and our car home but not what you need after a long flight. They found the key 2 days later and posted it to us.
So like you say take your keys with you or at least carry a spare set.