IMHO, Jim Baggotts book is by far the best I have found on the topic. Also covered off the deals between UK and US during this timeframe.
Well worth a read, not least to learn of Fuchs involvement in Russian Spy rings from that time, activity that saw the Rosenbergs executed for similar activity in the USA (the went to the chair).
Quite a dit on the UK Tube Alloys programme on Wiki.
https://en.m.wikipedia.org/wiki/Tube_Alloys