The British will hold, a British-Soviet war in the 1980s.

  That would be my thought as well, although it would also raise the same question as to why the Soviets are trying to conquer Britain and risking a nuclear response?  Possibly if it was dated at a different point, i.e. before France got a substantial nuclear force.  Unless you assume that for some reason, say the communist movement in France being more powerful and dominating the socialists rather than vice versa possibly coupled with Soviet espionage operations France folds.  [Don't really want to go that way as it kind of reinforced the old "cheese eating surrender monkey's" stereotype which given real history is insulting as well as inaccurate.]  Also there is a big advantage for Britain if for some reason France is neutral and unoccupied.

  How about if whatever causes US isolationism also causes pretty much a complete collapse of NATO and W Germany comes pretty much under Soviet control?  [Either by the communists gaining influence there directly or, using another old stereotype, a extreme right wing group gains power in W Germany prompting the collapse of NATO and then the Red Army moving in to "suppress the new fascist threat" as they would put it.  France also retreats into isolationism but Britain tries to maintain a protective alliance over the Low Countries and say Norway and possibly Denmark.  Because those countries wish to keep a low profile they don't want more than token, trip-wire forces present and when the Soviets march west their quickly overrun.

  That would allow a scenario in the 1980s, which I think is the time period you want and give two big advantages to a British defence.  France being neutral means that the Soviets can't use French bases, which was the real killer both for the BoB given the short range of a/c of the time and even more importantly in the B of the Atlantic they can't used bases in western France to threat the SLOC.  Also in such a circumstance the former BAOR would already be back in Britain with no time to deploy so the core of Britain's army is available for defence, along with those air units OTL based on the continent, probably using some of the now abandon former US bases in Britain.  Also any half-way competent British government [so avoid Thatcher ] would presume that in a future war Britain would be likely to be in this position and prepare accordingly.  As such the navy wouldn't be run down as much and plans made for defence of both the home islands and trade supply routes.  This gives a Britain that is essentially alone, other than probably Canada and Iceland and volunteers from some other locations, some hope of actually withstanding, at least for a while, the behemoth that was the Soviet war machine in the 1970-80s.  It still leaves open the question of why their trying to totally defeat a power with a significant nuclear deterrent.  [Definitely don't want to go along the route where some idiots have scrapped the nuclear deterrent, although for a while in the late 80's I think its actual status was rather dubious.]

  You would probably also need to avoid the Soviets using chemical weapons as their likely to be too destructive to any attempt to keep Britain functioning.  Even without them Britain is so dependent on imports by this time that unless you assume a substantial industrial/technological revival I can't see us lasting more than 6-12 months.  Especially as while their naval losses are likely to be much higher the Soviets will be able to replace them a lot more rapidly with their much larger military complex, at least unless they have one or more distractions elsewhere.  However I could see them losing a lot of air and naval units, although missile attacks will be a real problem.  Plus you could see a bloody nose for an amphibious/airbourne assault. 

  Possibly you could have the US again introducing a Neutrality Zone in the western and central Atlantic, which the Soviets respect to avoid bringing them in, which would considerably reduce the sea lanes that would have to be protected by the RN and possible assorted exiled naval forces as naval units would be the sort of ones that would most easily escape the Soviet invasion of their homelands.  [Plus the Dutch for instance might have units in the Caribbean that could be used by a government in exile.]  Possibly also some alliance task force might be operating when the war begins and a number of its units escape.

  Anyway, some initial thoughts on a possible scenario.  Still fear that ultimately we will go down or go nuclear but could give the Soviets a hell of a fight.