I've used Simply Airports in the past, but recently the quality has varied. Some cars are really clean and the driver drives safe and sound. Others it was like a rollercoaster ride.
There's always Uber, which is not bad.
My favourite is Wheely. They do higher end cars (think BMWs and Mercedes) and every time I've used them I've been impressed by the clean cars, courteous drivers, and safe driving.
Also they do fixed price to the airports, that can be prebooked in advance. From Clapham to Heathrow is only £40, which is a bargain for the quality of car and ride.
PM me if you're looking to sign up as a new Wheely customer - I believe if I refer you, you can get some money off your first ride.