ALREADY EXPLAINED WHY NOT
Boy, threads sure go a ton better when people read what's come before in the thread. Otherwise, threads can go nowhere. I've been seeing rather alot of that recently, and consequently lame threads. So, I'm reposting what I had to say, with the important bits bolded. I also have an alternate version of the challenge, which maybe can make progress now.
If Tube Alloys development had been separated, it probably would've stretched too long to have had any effect on the war, and Japan would've had to've been invaded. Bomb development was really, really, really hard, so a joint effort was needed for it be done on time. And, IOTL, it didn't arrive til mid '45, already so late.
Getting enough pure bomb-grade materials is still hard enough to be what keeps nuclear proliferation slow.
Sorry.... Now, there's an alternate interesting challenge, which is, thread, how could unified Bomb development have happened on Commonwealth turf?