If I could attempt my answer, taking the Queens Road Peckham-London Terminals ticket first. Your ticket is valid (at present):
-on all direct trains from Queens Road Peckham to London Terminals (which at present, gives you either QRP-London Bridge or QRP-London Victoria
-by the shortest route from QRP to each appropriate London Terminal station. As far as I can see, the 'appropriate' London Terminals for QRP are London Bridge, Cannon Street, City Thameslink, Blackfriars, Waterloo East, and Charing Cross. Vauxhall and Victoria in my view are grey areas (at this juncture anyway). I think we are all agreed that the stations on the other side of central London (Paddington going clockwise to Fenchurch Street) are all inappropriate
-routes within three miles of the shortest route are also allowed (I'll return to these two bullets later)
-by all appropriate mapped routes from QRP to London Terminals. QRP is a member of both London Group and Peckham Rye Group. With the London zonal cash fares, Peckham Rye group does pass the fares check rule, however because there is a common routeing point, this must be used.
Lets look further at shortest routes:
QRP-London Bridge 2.75 miles
QRP-London Cannon Street 3.5 miles
QRP-London Waterloo East 3.75 miles
QRP-London Charing Cross 4.5 miles
QRP-London Blackfriars 5 miles
QRP-City Thameslink 5.5 Miles
QRP-Vauxhall (grey area) 5 miles (via Waterloo East), for comparision QRP-Vauxhall is 9 miles via Clapham Junction which is hence an inappropriate route
QRP-London Victoria (grey area) 5.75 miles
and as I said, routes within 3 miles of each shortest route above are also allowed. I interpret this as a route from QRP to City Thameslink of 8.5 miles or less is allowed (when on a route to City Thameslink) but that an alternative route to London Bridge must be 5.75 miles or less (ie not 8.5 miles or less, ie you can't have the luxury of 3 miles more than the route to the furthest away London Terminal when you're travelling to the nearest one - but I suspect this is also a grey area).
If however someone else can clear this up either way, then QRP-Victoria (via the fast lines Victoria to Denmark Hill) is 5.75 miles. Note that via the Atlantic lines (ie calling at Battersea Park and Wandsworth Road) adds another quarter mile hence this would be more than 3 miles from the shortest route to London Bridge. Whether a SouthEastern RPI would really make something of this in the real world is another matter, though.
This is academic however if persons more learned than me believe that choosing Victoria as a London Terminal for QRP is appropriate. However, ATOC have recently published a list of
Appropriate London Terminals for each station and for QRP only London Bridge is listed.
We then need to turn to the question of what easements Southern/LO may put in place to ensure that passengers are not unduly inconvenienced by the fothcoming closure.
If wikipedia is correct (I haven't been following developments there that closely) all sections of the line will continue to have a service to either Victoria or London Bridge. Perhaps someone can say whether the Victoria to Bellingham service is definitely to happen?
If not, then in my personal view, it is wholly appropriate that passengers from South Bermondsey and Queens Road Peckham continue to be able to travel to Victoria (and stations en route) with a London Terminals ticket, which would perhaps be along the lines of "passengers from South Bermondsey to London Terminals may change at Clapham Junction for interchange purposes only". However, Southern/LO may not see it like that.
One for London Travelwatch perhaps?