All TL Depots sign all core TL routes (Bedford-Brighton and Wimbledon loop) plus 7oaks (not sure if Brighton do?). Different depots sign different bits for diversions.
As stated, all depots do Brighton - Bedford.
Blackfriars and Bedford also sign Blackfriars - Sevenoaks (via Swanley/Otford and via main).
All depots do Wimbledon/Sutton loop.
Diversionary routes include South London lines via Tulse Hill & Norwood Junction, Wallington lines via West Croydon, Brighton Mainlines via Selhurst (Streatham to East Croydon), mainline via Redhill (avoiding Quarry lines), Victoria to Bromley South via Chatham mains, Crystal Palace single via Birkbeck (Blackfriars depot only), East Croydon to Herne Hill via Clapham Junction/Factory Junction (Brighton only). Brighton also sign Wivelsfield - Lewes - Brighton as a diversionary.