There are two ways to interpret this question.
One is to ask why the Industrial Revolution was able to occur in Britain. The answer to this is that the British had the economic and political conditions, as well as the mineral and other natural resources that were needed to make industry possible on a large scale.
The second way to look at this is to ask why it was so successful--why people accepted industrialization and came to build their entire society around it. In this case, the answer is that it was simply the best way of making money and of making goods on a large scale. Of course, the Industrial Revolution had serious negative effects on society. At the same time, though, it was able to improve society in the long run by making more goods that people could use and by producing more money for the country as a whole. In these ways it, in the long-term at least, improved the quality of life for the average Briton. For this reason, it took root firmly and came to be accepted as the way to run an economy.