This doesn't help answer your question but ...
I remember reading that on a pound per mile basis the Heathrow Express is the most expensive train journey in the world.
It's not even the most expensive in London...
Covent Garden to Leicester Square - 270m between the stations - £14 per mile on PAYG Oyster - £29 per mile on a paper ticket.
Canary Wharf to West India Quay is 200m, so shorter distance, but different pricing zone - £12 per mile on PAYG Oyster - £39 per mile on a paper ticket.
