bob wrote:

(oddly I've had trouble buying a ticket from
Cambridge to Stratford International from Cambridge station, and
tickets from Cambridge to Stratford, routed any permitted, won't open
the gates at St Pancras (Kent), although the staff are happy enough to
let me through).

IIUC Stratford International for domestic services is a pick-up to
Kent/set-down to London only station. Certainly the buses to & from
Stratford regional are timed only to connect that way and I'd presume the
gates are working on the same principle (although the staff may either be
more relaxed about this or simply not know).