What I do now is as soon as I am on the HEx I fire up the national rail app to find out what time its due into paddington. I then use the Addison Lee app to book a car from paddington onwards to my destination. The drivers normally arrive a little early and wait for up to 10 minutes from the booked time in case of delays. They pull up at the rear end of the taxi queue so only a short walk from the train.

All the cars are smart new black ford galaxies, and it's cheaper than a cab. There's also no worries with finding your destination as the app containes masses of addresses to search through and they are linked to the drivers satnav etc.