The 3 mile rule wording from page one of the NRG in detail is worded:
NRG in detail said:
(1) the shortest route served by a regular passenger service or (2) a route no more then 3 miles longer or [...]
So it hinges on what a 'regular passenger service' is. Previous correspondence with ATOC suggest that this is a route which is served by trains that are timetabled to run at least once a week. So, look in the Network Rail
timetables (zipped), which were last updated 22/12/2014.
These are the tables you need:
Waterloo East: 199, 200, 203, 204, 206, 207, 212
Blackfriars: 52, 173, 175, 179, 182, 186, 195, 196, 199, 212
Find the latter pages which show services for mid-January to mid-May. There will be no services shown that call at both London Bridge and Waterloo East, or at both London Bridge and Blackfriars, therefore my interpretation is that they cannot form part of the
shortest route served by a regular passenger service. Things may change come May.
Others' interpretations may vary
Now, using the mileages shown in the first column from each table in same timetables, find the shortest route that services take. The shortest is 8.75 miles:
London Bridge - South Bermondsey - Peckham Rye - Denmark Hill - Victoria
Thus, you can take route no longer than 11.75 miles. This adds in:
London Bridge - South Bermondsey - Peckham Rye - Denmark Hill Clapham High St - Wandsworth Road - Clapham Junction - Battersea Park.
London Bridge - South Bermondsey - Peckham Rye - East Dulwich - North Dulwich - Tulse Hill - Brixton - Victoria
Furthermore, you can take any direct train. There is an argument that for a route thats only valid by virtue of the direct train rule, its only valid if the actual train you board is a service between London Bridge and London Victoria. See
this thread for a discussion on that.
This ticket would only be useful for journeys to and from intermediate stations. The savings over the obvious ticket are tiny, and I would say that it would not be worth the hassle you will get using it in this way. The routes during the long-running engineering works are a bit of a grey area, and it would be obvious you were trying to exploit a loophole.
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Forgot to add: There is an additional complication. Some season tickets that are usually valid between London Bridge and Waterloo East are valid on the Jubilee line during the Thameslink works, which could affect the shortest route (another grey area). According to
this page, for Southern and Thameslink passengers, this only applies to passengers
with London Terminals tickets. I believe that this is referring to tickets with an origin or destination of 'LONDON TERMINALS', but an argument could easily be made that it would apply to a ticket between two London Terminals.