I'd recommend trying UberXL (people carrier) or UberLUX (S Class / 7 Series etc.). If you're not already a member, download the app and use code jamesm283 to get a £10 credit (you may find better promotions online). I use them a lot and have always found them to be very good and competitively priced. Most airport journeys are fixed price and you can see where the driver is and when he's due to turn up.