I always use Addison Lee - large Ford Galaxy occasionally subbed for an E class - driver meets at time you set either x minutes after flight landing or set time (and you can book them about 40 minutes out if you don't want to do it until you are safely in the arrivals lounge). You can pay by card online and they have a good iPhone app to order cars when you are out/about in London (with typical maximum wait in central London being 20 minutes).