This book affected me so much I couldn't read the third story the first time I borrowed it from the library. Went back to it from curiosity when I was about 13.
It's called something like 'The Tomorrow Children' but I can't find it ammongst the more recent or more famous other works/media etc that has the same name.
Any ideas? It's three-part device was well structured, with the stories moving from a place near Manchester when the first bombs are dropped, and then the 2nd part is about the immediate aftermath. 3rd part is mutants.