There's the Heathrow Pod - little electric self-driving cars in dedicated lanes.
Image from ultra global PRT.
The Heathrow POD is free to ride between the T5 car park and Business Parking. It runs very close to the end of the runway so you can sometimes get an excellent view of planes landing. From within T5, follow signs to 'Heathrow pod'. It's a fun thing to do if you have a bit of spare time at Heathrow (particularly with kids).
The company's website has an interesting downloadable software simulator which you can use to plan and simulate your own pod network.
If you don't mind it being a bit larger then lots of airports worldwide have automated guideway transit systems, some of which aren't so different to self-driving buses in dedicated lanes.
Image by LERK
The BBC is now reporting that vehicles based on the 'pods' used at Heathrow are to be used for a trial project in Greenwich, where they won't have their own dedicated lanes:
The first driverless cars to be tested on the streets of London will resemble the electric passenger shuttles currently in use at Heathrow Airport.
The group behind the project is currently adapting the pods for use on the roads.
It has yet to unveil the exact design but confirmed that the adapted vehicles will not run on dedicated tracks.
Greenwich is one of four places in the UK where driverless pods and public reaction to them are being tested.
Trials will also take place in Bristol, Coventry and Milton Keynes. The £8m project is jointly funded by government agency Innovate UK and industry.
The Greenwich Automated Transport Environment project - or Gateway - will see seven driverless pods tested on the pavements around the Greenwich Peninsula, where the O2 Arena is based, from July.
London's first driverless cars based on Heathrow 'pods', BBC News, Jane Wakefield, 29 Jan 2016