What makes you think you were in a driverless train ?
Trains - at LHR well there is the HEX and HEC the passenger trains, both have drivers, well a bag of meat at the front. (Self described driver). Guys and Gals who all to frequently incur SPADS. (Mostly in the shunting yards) - I guess akin to ground movements.
Then the disused PAD - LHR baggage only line - and last (that I am aware of) is the very busy secured baggage system, so unless you talking about the staff car park bubbles ? More of a Disney ride I don't see it as these I don't think go between the terminals,
On the subject of automation, I consider nuke power stations would be a better system to start to automate, remove the people from the control room - consider the risk of an aircraft hitting a full stadium vs the risk of issue at a nuke power plant, - of course worse case would be the aircraft hitting the said control room.