... TfL» do however allow you to use Lancaster Gate for Paddington and Embankment for Waterloo and other tube stations which are within a sensible walking distance of the London Terminal (and the automatic gates will allow that too).
The logic isn't that clever I'm afraid. A magstripe ticket that allows cross London travel is good for any one entrance at a long list of stations, and one exit anywhere on the same list of stations.
So it isn't actually allowing you to use Embankment because it is near Waterloo, it allows it because it is on the list. (Being one of two stations appropriate for Charing Cross.) There is no test to compare the LU entry and exit stations with the National Rail journey you are making, so in extremis you could walk for instance from Paddington to Liverpool St, enter the underground and head for Victoria, leave the underground and then walk to Cannon St. Stupid, but the tickets would work.
Aldgate, Amersham, Baker Street, Balham, Bank, Barking, Blackfriars, Blackhorse Road, Cannon Street, Charing Cross, Ealing Broadway, Edgware Road, Elephant & Castle, Embankment, Euston, Euston Square, Farringdon, Finsbury Park, Greenwich, Highbury & Islington, Kensington Olympia, Kentish Town, King^s Cross/St Pancras, Lancaster Gate, Limehouse, Lewisham, Liverpool Street, London Bridge, Marylebone, Moorgate, New Cross Gate, Old Street, Paddington, Queens Park, Richmond, Seven Sisters, Southwark, Stratford, Tottenham Hale, Tower Hill, Vauxhall, Upminster, Walthamstow Ctl, Waterloo, West Brompton, West Ham, West Hampstead, Wimbledon, Victoria.
Paul
Absolutely right about the automatic gates and thank for finding the list of stations. Just because gate allows it doesn't mean it is allowed though. The law requires a cross-london transfer to be a reasonable (ie, at least not rediculous) route from one terminus to the other.