1. Brits were actively helping the US to build the bomb, if it weren't for the Brits we wouldn't have had the bomb until after the war. You can go online and find photos of British scientists working at Los Alamos.
2. All four parties involved had a nuke program, Britain, Soviets, US and Japan. Nobody knew how far Japan was along with their nuke.
3. Potsdam declaration said two important things
a. "We call upon the government of Japan to proclaim now the unconditional surrender of all Japanese armed forces, and to provide proper and adequate assurances of their good faith in such action. The alternative for Japan is prompt and utter destruction."
(this is the allies saying "we have the nuke and will use it")
b. The second thing is what wasn't said. No mention was made of the Emperor, in diplomatic speak this meant that the Japanese Emperor could stay.
Potsdam Declaration - Wikipedia
Ten days before Hiroshima millions of leaflets with the Potsdam Declaration were dropped all over Japan. By this time the US had powerful AM radio transmitters that could reach all of Japan and the announcers told listeners about the Declaration. Yes it was illegal for the Japanese to listen to US radio or read the leaflets but everyone in Japan knew of the Declaration.
The Japanese decided to "kill it with silence" a Japanese negotiating tactic. They didn't respond to the Potsdam Declaration.
Hiroshima was nuked.
Also when the Emperor finally declared he was going to surrender, military officers attempted a coup, they hoped to imprison the emperor and continue the war. The coup was defeated.
Also when Germany was defeated they sent all of their processed Uranium to Japan via submarine, like 100s of kilos of the stuff. The German uboaters decided to surrender to US forces and the two Japanese officers on board committed ritual suicide. Much of the captured uranium was used on the bomb dropped on Nagasaki.
August 1945:
News of the atomic bombing of Hiroshima reaches Ottawa just before noon on August 6, 1945. As a member of the Combined Policy Committee, Howe expects it. In a prepared statement, he says:
''It is a particular pleasure for me to announce that Canadian scientists have played an intimate part, and have been associated in an effective way, with this great scientific development.''
Three days later, on August 9, Nagasaki is bombed.
LOS ALAMOS, N.M. — When a captured Nazi U-boat arrived at Portsmouth, N.H., toward the end of World War II, the American public was never told the significance of what was on board.
The German submarine was carrying 1,200 pounds of uranium oxide, ingredients for an atomic bomb, bound for Japan. Two Japanese officers on board were allowed to commit suicide.
Two months later, in the New Mexico desert, the United States detonated the first atomic bomb, a prelude to the obliteration of two Japanese cities.
Unknown to many of the people who built those bombs, not to mention the public, Japan was scrambling to build its own nuclear weapon.
New Details Emerge About Japan'''s Wartime A-Bomb Program - Los Angeles Times
A Canadian scientist working on the bomb at Los Alamos accidentally irradiated himself. He died of radiation poisoning.
When Truman told Stalin America had the bomb, Stalin said, "Good, I hope you use it on them."