So how many bombs on the UK until they're as reasonable as the Japanese? ...
One or two, IF the Allies are convinced there are a dozen or more to follow. In the case of Japan there was a period of denial of the implications of the Hiroshima detonation, then came the Nagasaki detonation & no one in Japans government could realistically operate thinking the Allies had expend their nuclear arsenal. It would be much the same in the case of the Allies. One or two atomic detonations might be bearable, particularly if victory in otherwise less that a year out. Believing another half dozen detonation will occur in the next couple months is a different matter. If one is used vs Britain, & another on a key Red Army logistics hub, then the Allies may start considering how a good enough' defeat of Germany might be preferable to a 'perfect' defeat. So the leaders all have a sit-down, and some one opens with "It never should have gone this far."
The US will have atomic weapons within the year. Germany now lacks most of its critical resources needed. Its industry and population crippled. Maybe a deal can made??? Or would the Allied populations see continued war more sane than allowing the nazi regime to survive?