Well the thing is I dunno how the navy would react to a coup: also I doubt you could get a sub into the Clyde remember when it got stuck a few years back?
100% they wouldn't, nobody has even ever prepared to use nukes in this country they mostly just exist to wave at the yanks in-case they threatened to take theirs away and to act as a jobs programme to get subs built.
I unironically didn't consider the terras: tbh most of them tend to be either rural proles (while he was a trucker-driver my uncle was a terra, he's a weird one) or middle class LARPers. IMO they wouldn't support a coup instinctively purely because they would be too moralist about it (the middle class lot) or they are weirdo libertarians (the rural proles). Regardless the TA centres don't keep the terras there they are scattered all over the place (unlike the army who obviously live on barracks). It would be difficult to even organise the terras for a coup attempt, and besides you never use reservists for this exact reason (you have to give them a reason to call them up, which kinda gives-up the ghost. In turkey they used conscripts and told them it was for anti-terror purposes and when they found out it was a coup they basically surrendered).