have been using it from StP to City Thameslink, and is accepted both ends by the machines,
St Pancras is a terminal from the north, and City from the south. They are both London Terminals (and with the advent of HS1, a ticket from a Kent area station would be valid at both). However, a London Terminals ticket is
not valid at Farringdon - even if just passing through the station, such as the manner in which you describe.
In my view it's the same as using Waterloo East to London Bridge to get to the City as an alternative to the Waterloo & City line - something hundreds of people do every day!
I'll make a point of asking someone at the gates and find out what they say and let you know!
It depends on the ticket held here, if it is from a SE London/Kent station to London Terminals then fine. Same goes for a SWT station (and going into Waterloo*).
If, however, a U1 ticket is held then the situation isn't so clear cut. These tickets apply when the first or last leg of the journey is made by LU services (or an approved 'interavailable' route with NR). I don't believe any interavailable route extends to Waterloo East (although I will happily be corrected on that), so such a ticket would not be valid to London Bridge.
*It has been documented elsewhere that a London Terminals ticket does not cease to be valid at the first London Terminal you arrive at in the case of that cluster, on the proviso that you stay within the cluster: Waterloo, Waterloo East, Charing Cross, London Bridge, Cannon Street, Blackfriars, and City Thameslink.
e.g. Clapham Junction to London Terminals is valid at any of the above locations if travelling into Waterloo, with onward travel via Waterloo East (and changing at London Bridge, if necessary). Of course, this ticket is also valid into Victoria, and London Bridge on a direct service.