I'm exploring possible 'utopian' outcomes to this situation. We invariably think of the aftermath of nuclear holocaust as exclusively dystopian - could a 'better' world have emerged in the 60 years since the crisis? Is there a possible scenario where England would have come through 'fairly unscathed'?
It depends on the exact meaning intended for the word “habitable”. But I would suggest that the world (or at least many parts of the world) would have remained habitable and inhabited. This doesn’t mean to say that life would be pleasant or that billions would not die immediately and in the years following for famine, disease and radiation poisoning, but human life would not have been exterminated.
This would be especially true for out of the way places. For example New Zealand, even if the largest cities were attacked (debatable) a great deal of the country would remain very habitable. Yes no doubt there would have been increased levels of radiation, hardship and death, but the majority of the fall out would have been in the northern hemisphere due to the general nature of air circulation patterns and the fact that the primary protagonists were based in the northern hemisphere.
Response following the change in the question of habitation from the "World" to "England".
In any global nuclear exchange it seems likely that all allies would have been drawn into the conflict and would have become targets. However there are other less likely but possible scenarios where the nuclear exchange was more limited, less wide spread or less effective due to target priority sequencing, pre-emptive strikes on missile launch sites, subterfuge and misinformation, technical problems or the whims of those in charge under abnormal levels of stress.
Regardless of that billions would die as the world’s trade, food production and most other systems collapsed. But some life would continue even in England. After a few decades the nuclear winter should fade and the very few who survived in remote areas from stored food and scavenging might be able to start growing things again.
Large swathes that were bombed, and their downwind fallout zones, will return to habitability fairly quickly -- weeks, not years. That's why people live in Hiroshima and Nagasaki today. A few locations close to impact sites and downstream concentration points will take longer.
Nuclear weapons (expect for neutron bombs, of course) are designed primarily for the blast effect. The radiological contamination and fallout are a consequence (or a bonus, from some perspectives), not the goal. Most of the radiological products of nuclear weapons have short half-lives, quite unlike the long-half-life waste from power stations.
It will take years to return to background levels, but only 4-8 weeks before salvage crews in most areas won't suffer radiation sickness. Those locations very close to ground zero will take longer...but there shouldn't be much left to salvage in those blasted zones.
That's a rather wide window of "habitability" -- parents of growing children, for example, might define the term much more narrowly.