So Russia has weapons that can take out any target in Europe without being intercepted.
So they claim and it's possible, though not guaranteed. It's also not a new situation, that's been a concern for decades; it's such a concern, most of Western Europe has been strongly invested in an organisation building a military alliance to make Russia question using such weapons, it's called NATO.
Question: if they target the UK's store of nuclear warheads with conventional hypersonic missiles like the Hazel, would those nuclear warheads detonate?
It's highly unlikely - the protocols aren't open-source, but just from a safety point of view - that the warheads are armed in storage. That is to say that the explosive spheres that are used to compress the fissile material, and the fissile material itself, will not both be stored within the warheads in storage. The chances of any other explosive force (such as an ICBM detonation) operating in a fashion that would create a fissile chain-reaction to cause a nuclear detonation is unimaginably small.
There may be some active warheads at the HMS Neptune if a boat is in for reloading, but probably not at the back-up facility in Plymouth. Again, even if the warheads are armed, the chance of a missile explosion detonating the nuclear warhead is incredibly remote, although it could send contaminated materials airborne in the debris.
Of course, that's presuming the Russian missiles actually work, and actually go where they're aimed, and aren't targetted as Russian missiles seem to be lately at hospitals, schools, power infrastructure and other illegal civilian targets.
O.