For the purposes of "Not Via London", the relevant stations that have to be avoided are those in the London routeing group, namely:
- Blackfriars
- Cannon Street
- Charing Cross
- City Thameslink
- Euston
- Fenchurch Street
- Kings Cross
- Liverpool Street
- London Bridge
- Marylebone
- Moorgate
- Old Street
- Paddington
- St Pancras
- Vauxhall
- Victoria
- Waterloo
- Waterloo East
So, for example, a journey from Watford Junction to Southampton Central that used the Southern service via Kensington Olympia to get to Clapham Junction would be perfectly fine on a ticket routed "not via London" if one existed for that journey. (Upon checking, the relevant tickets are actually routed "via Kensington Olympia"). What you couldn't do on such a ticket is Watford Junction - Euston, tube to Waterloo, then Waterloo - Southampton Central.