I have some doubts about that; what I've read indicates that the Soviets really didn't think that their ABM system was going to be very effective at all. Rather, they felt it would be the opposite: it would only stop a handful of weapons from getting on target.
This is a fairly classic "other side of the hill" problem - the British were convinced that the Soviet system would work, and the Soviets were convinced that it wouldn't. In terms of the British decision making, it's what they believed which was important.
Most open source discussions regarding Soviet nuclear war fighting assume a double strike on SAC bomber bases a 25mT airburst AND a 25mT ground burst. Assuming a force of 160 aircraft (the number necessary to match the max potential of "surged" RN SSBN assets of two SSBN, the patrol boat and the along-side, prepping for patrol boat, with full load of the UK's deterrent stockpile) that would be 40 sites receiving 50mT of attention. Considering the fall-out from a 25mT ground Burst and the weather patterns, is there enough territory IN the UK to absorb that level of hit and have any reasonable number of survivors just from the counterforce strike?
The U.S. has lots of open space to put major assets where heavy fall-out will mainly land on nothing in the case of a counterforce strike (a full strike is, of course, an entirely different matter).
UK nuclear doctrine is very different from US nuclear doctrine. It isn't about fighting and winning a nuclear war - we know that in pretty much anything beyond a token nuclear exchange the UK will be rendered unrecognisable and about the only thing left of the original state will be the geography and probably the language. That's where you get things like
Threads,
When the Wind Blows and the CND - that reality affects the UK vastly more severely than it does the USA.
That means there is relatively little planning for fighting and winning a nuclear war - instead it's about ensuring that a limited nuclear war involving only the UK and one other country becomes a general one, explicitly with the US getting involved. The defence against a counterforce strike is not to be there when it lands (much easier for a bomber than an SSBN - you need more than 4 minutes to scramble one of those, so are more reliant on political warning of a threat).
This also feeds into the counterforce strike the USSR could use - they had relatively limited number of the extremely powerful, high accuracy missiles that were designated against SAC in the counterforce role. If they use them against Bomber Command, they're hideously vulnerable to a SAC counter-strike should the Americans become involved - and the British will be doing everything they can to get the US involved, up to and including shooting the American holders of dual-key weapons and firing them themselves (there was a plan in place to do exactly this with Thor, in the event of a nuclear war involving the UK but not the US).
Essentially you're assuming that the UK would have to replicate SAC in order to make use of bombers, and that just isn't true - they were both trying to do different things and have a different position from which to carry out their mission.