Does anyone know: if you have a national rail ticket coded for
cross-London travel will it work at any of these, or just the two
(typically) that are adjacent to the appropriate national rail
termini?

It's my belief, based on experience and some knowledge of the underlying
software, that any NR ticket with cross-London validity works for any
(one) journey between any two of these stations.

If the tickets were to be restricted to a truly 'appropriate' journey,
either the ticket would have to list (on its magstripe) all the NR
stations 'appropriate' to both ends of the cross-London journey, or the
barrier would have to be able to deduce that information, given the (NR)
endpoints of the journey. The former would (in extreme cases) need more
capacity on the magstripe than exists, and the latter would probably
require the barrier to have access to the entire routing guide.

By 'extreme cases' I mean something like Birmingham to East Croydon,
where you could arrive at any of several London stations and travel to
any of several others. If you wanted to make it truly 'appropriate'
then the validity of the ticket on LU would have to depend on which NR
terminus you actually arrived at, and validity on NR leaving London
would have to depend on where you left LU (eg if you got off the tube at
Charing Cross, then it would be 'inappropriate' to take an NR train from
Victoria). I'm quite sure that isn't the case.

There remains of course the possibility that even though the barriers
allow it, the ticket isn't actually valid for the journey.

Peter

--
Peter Campbell Smith ~ London ~ pjcs00 (a) gmail.com