Via Barnham just means you must travel through Branham.
Not London Just means you must not travel to or through Victoria or Vauxhall (which precludes Waterloo) it is intended to be essentially a via barnham and or Clapham Junction, although on some flows the routing guide may permit routes via Gomshall which falls into 'Not London' but outside of 'via Barnham' .
Although the RG prohibits such routes on some flows and I'm unsure if there is intention to prohibit or permit such routes through Gomshall, and TBH I don't think SN or SWT have thought about it turning it into a bit of an oddity.
I am ofcourse just referring to flows from the SWML to Southern priced destinations on the East Coastway and Kent etc. and the above does not apply to most other flows.
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I'm unsure that it is meant to be valid via Victoria, however I do not see anything preventing it being valid that way. So I would say go head but expect to be questioned.
Since it is a Southern-priced flow, I don't think this fare will survive for very long without further restrictions being added to the Route field.
Given that my choice would be to change a London Bridge and Three Bridges or Redhill (or Brighton but I tend to find the station overcrowded most of the time, Gatwick/ East Croyden are also options) unless there is a specific reason to go to Victoria.