Potential catorgories for the other two TOCs:
Great Western (Brighton-Southampton, including Pompey, Redhill-Gatwick)
South Western (Havant-Soton, including Pompey)
Thameslink (Sutton Loop, London Bridge-Brighton)
A couple on the West Coast, but these are ruled out by the lack of OHLE.
South Eastern (Redhill area, London Bridge area, Victoria area)
Reigate (served by Great Western and South Eastern)?