No it wasn't. https://en.wikipedia.org/wiki/Tube_Alloys
Post WW2 the USA (for a bunch of quite interesting reasons) excluded the British. But, of course, the British had acquired a lot of knowledge from the program and were able to develop their own bomb.
https://en.wikipedia.org/wiki/Klaus_Fuchs
Sure, non-US nuclear arms would have most certainly happpened either way, but exfiltration did presumably at least accelerate the timeline.
No it wasn't. https://en.wikipedia.org/wiki/Tube_Alloys
Post WW2 the USA (for a bunch of quite interesting reasons) excluded the British. But, of course, the British had acquired a lot of knowledge from the program and were able to develop their own bomb.