When I think about it, it seems for me at least that Britain would be a country with quite a logical case for IRBM's instead of manned bombers during late 1940's and early 1950's.
By early 1950's it was clear that Britain would be a charred toast in a nuclear war, so nuclear warfighting, the forte of a bomber force, is irrelevant, just deterrence is necessary. At the same time it seems that new bombers will get exponentially more expensive while Soviet Union is making better and better SAM's.
What advantages IRBM could have? First, the distance between London and Moscow is just 2500km's, so one does not need an ICBM to cover it. Second, reaction time even with liquid fuelled rockets could be low, and in fact, with 1950's accuracy one might have silos which could ride out the attack, just like historically planned with British IRBM's. Third, defending against IRBM's is mightily more difficult than against bombers.
Could we have a POD where instead of V-Bombers RAF's V-force is equipped with, say, improved Canberras suitable for a nice one way flight instead, intended to serve until IRBM's are operational in late 1950's? Maybe WSC Churchill committing himself to the project, not just because it's military useful but also for prestige value, having the most advanced military gear on the planet, better than anything Americans have, and of course some scientist might have an idea about an artificial satellite. An advanced missile could be also used as a negotiating point to get more advanced nuclear bombs from the US.
So, can we have a British IRBM in service, by, say 1956? First with Violet Club equivalent warhead, with Yellow sun from circa 1959 onwards?
Bonus points if Britain can develop a liquid fuelled IRBM for naval use, like Soviets did. Extra bonus points if Americans built it with license. Super bonus points if French buy it too.
Even more bonus points if someone has already written a TL out of this...