That wasn't because the British thought the majority of their warheads were duds. It was because they thought that several would be shot down by the ABM system as well as the prerequisite allowance for failures.
I also think that you've got to take into account the difference in intention of a nuclear deterrent; the UK arsenal is enough to be able to start a nuclear war – but not enough to fight one in any meaningful sense. As such, all it really does is act as a ‘diplomacy multiplier’ in that it makes the guys in the Kremlin pick up the phone when international tension is really bad. That, and (hopefully) remind people that any attack would be - to put it mildly - costly.