If by "early understanding" you mean the physics then the work prior to World War 2 was so multi national it is kind of hard to unravel which nation contributed what in the way of understanding....early on at at the start of it all you have the likes of Chadwick and Thomson, and I'm pretty sure a Brit, or Brit supplied (see below) explosives "expert" was heavily influential in the design and/or engineering of the Plutonium implosion weapon but darned if I can remember the name at the moment. IMHO the best primer is probably Richard Rhode's on work "The Making of the Atomic Bomb" but it's tough following all the nationalities.
Of course you also have to consider the influence of those Europeans who Britain sheltered prior to WW2 who went on to make significant contributions to the A bomb (e.g. Fuchs), and the H bomb (e.g err Fuchs....for both sides).
It's a complex bit of history, that's for sure.......Rhodes has done as good a job as anybody at depicting what went on...