Specifically, I'd like to hear what Americans and British citizens at home thought of this act. I'd imagine there was some horror at this, but then again, I've never lived in the States during a time of total war, so I don't know if they were thinking "Whatever gets our boys back home" or something along those lines.
Well firstly it's pretty hard to generalize over a huge population like that. Nonetheless, news of the atomic bombing was greeted enthusiastically in the U.S.; a poll in Fortune magazine in late 1945 showed a significant minority of Americans (22.7%) wishing that more atomic bombs could have been dropped on Japan. We must remember the political climate of the time.
Secondly the aftermath of the atom bombs was heavily censored by the US Army. The initial positive response was supported by the imagery presented to the public (mainly the powerful images of the mushroom cloud) and the censorship of photographs that showed corpses and maimed survivors. They publicized and celebrated the powerful blast but worked to suppress information about the bombs’ radiation.
All journalists were banned from entering the zones of destruction so very little information on the ground reached the public. One journalist however made it through: Wilfred Burchett who bravely travelled to the devastated cities alone. He published an article by the Daily Express newspaper in London on September 5, 1945, entitled "The Atomic Plague", the first public report to mention the effects of radiation and nuclear fallout. Burchett's reporting was unpopular with the U.S. military. The U.S. censors suppressed a supporting story submitted by George Weller of the Chicago Daily News, and accused Burchett of being under the sway of Japanese propaganda. Laurence dismissed the reports on radiation sickness as Japanese efforts to undermine American morale, ignoring his own account of Hiroshima's radiation sickness published one week earlier.
With time the effects of the nuclear weapons could no longer be fully disguised, as more reports and accounts of the events started to come out. The American Military portrayed the nuclear bombings as necessary and just, which meant that many people still viewed them positively, but of course a substantial amount started to become aware of the sheer horror and with time an anti-nuclear movement started to grow. However the attitude of military and political leaders continued to be shockingly positive, and the world has had very many astonishingly close misses with nuclear war since then. This has continued into the present day, most recently with Obama pledging to upgrade and maintain the US nuclear force at a cost of $1 Trillion over the next decade.
There are many sources you can check out about the bombings, starting here, and if you google around. https://en.wikipedia.org/wiki/Atomic_bombings_of_Hiroshima_and_Nagasaki#Depiction.2C_public_response.2C_and_censorship
http://www.counterpunch.org/2014/08/01/censorship-and-myth-making-about-hiroshima-and-the-bomb/
http://www.theguardian.com/commentisfree/2014/aug/06/hiroshima-day-nuclear-weapons-cold-war-usa-bomb