I don't really know much about how general people around Europe would have reacted towards Hiroshima and Nagasaki, however I can help a little with how the scientists of the German Atom Bomb project reacted.

The scientists who had though to have been working on the German Nuclear Program had been detained during Operation Epsilon and then interned in a bugged house in England. During that time, the reaction these scientists had towards the Bombing of Hiroshima was recorded.

Obviously, they all have differing opinions on the subject, some for example, such as Otto Hahn, who had discovered Nuclear Fission and won the Noble Prize in 1944, but otherwise had no part in the program, was glad that the Germans never achieved making the bomb (he even considered suicide, believing himself responsible.) Others however, where dismayed they had failed.

They all seem to wonder why Germany didn't manage to build the bomb, comparing that project to the thousands of people working on the V1 and V2 rockets, as well as talking about the relationship between Germany, and the Scientists, compared with how America treated there project, because they say the Germans didn't trust the Scientists working on the project, and the project would have been difficult to push through because of this, especially as they say the German Government wanted immediate results, not having to wait a long time until the project was complete.

They also had conversations about what went wrong with the theory behind the German Project (and Heisenberg soon worked out how to build the bomb, after hearing of the dropping of the American Bomb).

If you want to read more about it, main source is Operation Epsilon: The Farm Hall Transcripts, which has an extract here which says which books you can read the whole transcript in.

One particular lack of reaction by a European might be interesting to you. The sitting pontiff, Pius XII, made no public comment on the atomic bombings in the immediate aftermath of the events. How is this possible, given that a new type of warfare had just debuted?

Well, for the pope, Hiroshima and Nagasaki appeared little different from the other area bombardments of WWII. The Vatican position was consistent: from the advent of such tactics in WWI, to the new methods unveiled in the bombing of Guernica during the Spanish Civil War, to the many horrific bombings of WWII both in Europe and in Japan, the Church had condemned the general targeting of civilians by aerial bombardment. The Vatican failed in its multiple attempts to have the combatants halt or curb their bombings. Vatican diplomats did not lodge a protest over every individual bombing, and that included Hiroshima and Nagasaki.

To be clear, the pontiff understood the issue at hand. In 1943 he voiced concerns over recent advances in nuclear fission (though he overestimated the effects). But to the Church, killing tens of thousands of people with one weapon or with thousands of weapons was basically the same act--targeting noncombatants by aerial bombardment.

Re: Churchill — he was one of the ones who helped make the bomb, and the assent of the UK was required (by the Quebec Agreement of 1943) before it could be used. They gave it readily. The UK issued a press release by Churchill (even though he was no longer PM at that point) hailing the bomb and its use.

You can read the UK statements about the bomb here.

Churchill himself did urge Truman to consider easing the "unconditional surrender" requirements at Potsdam, with the idea that the war might be ended without using the bomb, but he backed off it when it became clear that Truman was not interested in such a thing. This is discussed in Tsuyoshi Hasegawa's Racing the Enemy among other places.

One thing that has not been mentioned in some of these (incredibly well thought out replies) is that the true horror of the bombs were not fully understood at that time. If all that the bombs did were kill indiscriminately at the instant they were detonated, they would be nothing more than supremely powerful military tools, although their use would still be highly controversial as it's impossible to even attempt to avoid civilian death when using one. Hiroshima and Nagasaki were selected as targets for the reason that they were largely untouched, and therefore were sacrificed as demonstrations to will the Japanese into surrender-- The additional horror of the radiation created by their detonation was not understood until later on.

What terrifies me is that there were early plans for the invasion of the Japanese mainland that called for using nuclear weapons on the landing beaches to prepare them for the invasion forces, and then land Allied troops into this irradiated area.