Was there much protest at the time about the closure?
Oh yes there was plenty but too no avail.
Yes, by 1963 The Pines Express was no longer running over S&DJR▸ metals. The last time it ran via that route was 8th September 1962.
Very much an organised rundown, with lots of other railways in the same period. The Devizes line closed completely and the Melksham line to passengers the month after the Somerset and Dorset. The year also saw the end of passenger trains on the Waterside line, to Yeovil Town, at intermediate stations on lines which are still open (such as Wilton South station), Taunton to Barnstaple, the Cowes line, Wroxall and Ventnor on the Isle of Wight.
With so much going on, protests with regard any single line were in some ways "just another protest", though there were some lines threatened but survived through this period. Without "online" and with just a handful of TV channels, the media and the voice of the individual had very different metrics in those days.