The "why not China" part of the question has been answered before in threads like this one, though I'm sure there's always room for contribution.

I don't think the "why Britain" part of the question has been answered in depth though. At least not to my knowledge. Why Britain first, and not France, Germany, Spain, the Netherlands, etc.

First, it's worth noting there were two phases in the industrial revolution. The first was a revolution in terms of mechanizing certain industries - such as textiles - through the use of steam power. The second, arguably more important phase was the mass production of cheap steel which facilitated the construction of railroads and steamships that created a transportation revolution for both people and goods.

With regards to the former, the easy answer really is that it occurred right after the Napoleonic Wars in the 1830s, and Britain alone was pretty much spared from having its heartland ravaged by the conflict against Napoleon. Everyone else was to some extent still rebuilding or dealing with the after-effects of the war. The British by contrast could now focus on investing on new things to build on top of their intact country.

With regards to the latter, it's arguable that everyone - but most especially the United States - could have potentially caught up by this point; particularly since the United States had in fact built more railroads than the British by 1870 (and would overtake the British economically by the end of the century). However, again, the war factor is at play here - the Franco-Prussian War occurred in 1870, while America went through the Civil War in the 1860s. Britain was involved in some conflicts in this period - notably the Crimean War - but again the British heartland was essentially untouched. Indeed, it's arguable that the British lead in steam ships - which was barely maintained into the 20th Century - only happened because the Civil War pretty much destroyed the US merchant marine industry.

In short, it "started" in Britain primarily because it was the least affected by the Napoleonic War, but everyone in fact managed to catch up by the 1870s (barring interruptions due to war) and the US would even surpass them altogether by the end of the century. It's not really a demonstration of British exceptionalism; and more of British historians having rather rose-tinted glasses about Pax Brittanica.