Manuel,
The UKs free fall nuclear bombs wouldn't have come into it and certainly not under START/SORT. It was a unilateral decision by the UK Government to retire WE177 early and have that sub-strategic mission incorporated into Trident.
Those WE177s assigned to NATO would have been tactical munitions and not covered by the likes of START. The UK had no heavy strategic bombers to carry the higher yield WE177Bs. The US and the Russians didn't have treaties over tactical nuclear weapons but instead had Presidential Nuclear Initiatives. Those initiatives and pledges were already in hand to reduce the number of tactical nukes. It resulted in some 3,000 US tactical nuclear weapons not covered by START being destroyed.
TJ