Just checking 1963 timetable.
In the up direction there were Guildford via Cobham trains at 6.59, 7.29, 7.49 which were then Wimbledon only. The 7.29 must have used the Up Fast.
To my surprise, in 1959 there wasn't a 7.49, but the first up stopper from Basingstoke called at 7.53, giving NM a steam train non stop to Waterloo - I suspect that was primarily to set down staff heading for the London District offices Wimbledon?
Back to the topic - the times were unchanged in 1966-67, but I'd be fairly certain the 1967 timetable revision took out the "fast" trains and that's when the island platform ceased regular use. The timetable I knew well in my Waterloo days (late 70s) was basically unaltered from 1967...