It is generally agreed that the industrial revolution began in Britain - Britain was the first country in the world to see a sustained increase in economic growth per capita (along with population growth). And a number of important inventions and improvements were first commercialised in Britain,  in textiles, iron production, steam engines, precision engineering and steam-powered railways. 

That said, the Netherlands saw persistent GDP growth even earlier in Britain, and early developments in industry, with a period of intense technological change from the middle of the 16th to the middle of the 17th centuries (van Zanden, 2012, page 128). The Dutch GDP growth rate then was slower than in Britain during its industrial revolution, but it was happening. 

And there is a considerable debate in the economic history literature on when and why Europe's economic outcomes diverged from Asia's, with a number of arguments being made that it was quite late. To quote O'Brien's summary review:

... recent historical research on Asia has produced some partial, regionally specific and still inconclusive and defective evidence to suggest that standards of living in Western Europe and maritime provinces of China and South India may not have differed perceptibly much before the late 18th century [emphasis in the original]

It appears that technological developments were generally spread across Eurasia and into Africa, up until Britain suddenly started accelerating.

So why was Britain first? There are numerous theories as to why, and I don't think the question will ever be definitively answered, since it's something that only occurred once. It may have been basically chance, that once the underlying technologies reached the right level to enable a GDP take off, Britain happened to be the first place to combine a supportive geography with supportive institutions (e.g. literacy rates) and a relatively supportive and peaceful government. But who knows, perhaps tomorrow someone will publish a paper that changes my views entirely. 

Sources

Engerman & O’Brien (2004), “The industrial revolution in global perspective”, https://pseudoerasmus.files.wordpress.com/2017/04/engerman-obrien-2004-cehbv1.pdf

Professor Patrick O'Brien, review of Ten Years of Debate on the Origins of the Great Divergence, (review no. 1008) https://reviews.history.ac.uk/review/1008 Date accessed: 19 October, 2020

Persistent but not consistent: The growth of national income in Holland 1347–1807

JL Van Zanden, B Van Leeuwen

Explorations in economic history 49 (2), 119-130, 2012, http://www.academia.edu/download/47531263/j.eeh.2011.11.00220160726-26569-72lgz.pdf

Wright, Chris, Causes of the Industrial Revolution: An Overview, January 2020