I have been lucky enough to visit nearly all the fast line platforms (ECML, MML, WCML, SWML, GEML, GWML, Brighton ML, Chatham ML etc) in the Greater London area as part of my all platfoms gig. With few exceptions they are all available to be used during times of engineering and at times of disruption. In pretty much all cases i have experienced, one, (sometimes more) of the fast line gates have been open at staffed stations upon boarding/alighting. Often its just the gate nearest the entrance/exit. Most but not all of the others are unlocked and available too but you have to do operate them manually. Some stations operate a locked gate policy so only one gate is available for use.
With unstaffed stations further out of London its more of a mixed bag and where i am on the first train of the day (nearly always Sundays) i have had to open the gate myself more often than not.
As always with all things railways there are exceptions, and one late night escapade at Wandsworth Common P4 would have seen my me locked out of the station if i had gone the day before. The passenger who alighted with me said that the previous night he had to scale the rather high fence to gain the footbridge with which to exit the station. 2 others with bikes had to scramble back on board and come back from Clapham Junction to alight in P3 which did have access to the footbridge. I thought all London stations were manned until the last train but not the case on this occasion it seems.
Quite a few fast line platforms are not timetabled during engineering works any more but most here would know what these are. New Cross Gate, Hadley Wood, Queen's Park and Wembley Central are all listed in the Sectional appendix (i think) but Acton Main Line, Taplow, Hanwell, New Malden and Esher are not. I may have missed one - apologies.
On Sundays, the gates are definitely unlocked at Wimbledon as I've used them before. Never tried opening the gates on other days though.
I have used P7 at Wimbledon on a scheduled service Sunday mornng post 10am. The gates were specifically unlocked on this visit just 2 minutes before the service was due - possibly as it was a one off use of the platform that day, whereas in the current timetable there is use hourly on a Sunday on services for Basingstoke. I have still to do P6 however but Sunday opportunities do exist i understand so it would make more sense that the gates remained unlocked on Sundays at the moment.