Some good news is that modern nuclear weapons (H Bombs) don't have nearly the same risk of fallout. The kind that we're used on Hiroshima and Nagasaki worked through fission: so taking really heavy and unstable elements and breaking them apart to release energy. They are very inefficient and the blast would distribute a lot of unreacted waste (that's the fallout).
H-Bombs have a primary fission stage and a secondary fusion stage, where the fission energy is used to cause a bunch of heavy hydrogen to fuse, releasing huge amounts of energy. The amount of actually radioactive material in a H bomb is far lower, so there's no so much a of a problem of fallout.
That said, they are many many times more powerful than a fission weapon. That could be a plus, given you're very likely to just die and you wouldn't have to live through a flattened UK, could be a minus because... Well, you're dead. Depends if you're a glass half full person or not.
My father was in Coventry in the 80s when they accidentally set off the early attack warning. He rolled over and went back to sleep, as did the rest of the population. Apparently, a police officer had phoned up the speaking clock, and it had mistakenly set off the warning (as the alert system piggybacked on that infrastructure.) Personally, I would too. By the time protect and survive (and I'm veering very far off topic here) became public knowledge, I imagine most people were numb to nuclear armageddon by that point (as is evidenced by interviews with people at the time being asked what they would do, and a top answer being "finish my pint"). Protect and survive is a gem, though, really. I love the note about caravans which is basically "idk have fun being dead I guess".