After the war, the US froze the UK out of it's nuclear programme.
Which considering how much the UK had advanced the US project felt like a kick in the teeth - the signs were all there.
Anyway, post war you weren't anyone if you didn't have an H-Bomb. Only the US and USSR managed to make one. Without access to the US research, the UK wasn't able to build one.
Only we did - which means we independently were able to do the very extreme research and engineering needed. Putting us in the same league as the US.
It was after that the US relented and readmitted the UK to it's nucleal programme.
This was back in Eisenhowers day. (I think Kennedy did the Polaris deal).
https://en.wikipedia.org/wiki/British_hydrogen_bomb_programme#
Bomb making is (much like the Apollo programme) really extreme engineering. The physics is well understood.