Any of the "regular" companies like justairports simplyairports will be able to do what you want - though ensure you ask for a big enough car.

But don't assume that you can't get to your accommodation by public transport - quite a few stations do have access suitable for buggies or you might be able to use the Tube part of the way then take a bus. The journeyplanner on tfl.gov.uk can tell you the best way