The point of NATO was not to win a cold war conflict but to deter the Soviet Union from starting one. The purpose of the BAOR (until quite late in the day) was not to stop a Soviet attack but to persuade them that the loss of the BAOR would be considered serious enough that nuclear weapons would be used. Just like the US ground troops in Europe the BAOR was a hostage/tripwire intended as a sign of commitment to the alliance and to Western Germany in particular. This role could not be fulfilled by naval or air forces based in the UK, so reducing its manpower would weaken the alliance, and was why a political crisis in NATO erupted every time the UK sought to redeploy troops from Germany to the UK (to reduce foreign exchange costs). The question of how much money needed to be spent on equipment for the BAOR is a much more open one, but military pride and political credibility played roles here, while the suggestion above seems to be that manpower was a key constraint in any case, as was a treaty signed by the British promising to maintain certain troop levels on the continent.
In other words a weakened BAOR would make sense from a purely British perspective as long as everyone else continued to believe the UK would risk a nuclear exchange to defend Bonn or Berlin, but this condition probably wouldn't hold as the belief would probably be affected by a reduction in the BAOR in an unquantifiable way. Every other NATO member faced a similar dilemma, namely how much could they reduce their predeployed forces without damaging their perceived commitment to the alliance, but the perceived commitment of the US (especially) and the UK were fundamental to the alliance working so once in office politicians tended to be reluctant to make changes with a huge but unquantifiable risk attached.
