849C were indeed on the Ark, but not in 1967 as they were disbanded shortly after they flew off Ark for the last time on 1 October 1966, having joined her from September 1961 until February 1964 and again from November 1964 until 1 October 1966. Ark was in refit from the latter date until early 1970 - and the Gannets were then provided by 849B Flight.
If the person in question was with 849C but physically at Brawdy in 1966 then the timeframe is limited from around early June 1966, when the Gannets disembarked to Brawdy from Ark after arriving from the Far East, until just after 1 August 1966 when they re-embarked for Exercise Straight Laced and the final flying sessions thereafter until they went back to Brawdy to disband in October 1966.