It is still debated among economists and historians why exactly Britain was the first country in the world to industrialize, and if you ask different people you'll get different answers. However, there are certain definite advantages Britain had that may have contributed to their early industrialization:
1. Britain was already rich by world standards at the time. While their level of income seems small to us today, it was larger than that of most other countries in the world; people had enough income to be consumers and investors rather than simply working to survive.
2. Britain has one of the most stable, long-standing governments in the world. Whereas most countries go through a revolution every few generations, Britain has undergone a process of gradual reform that has preserved the same core---a constitutional monarchy with Parliament as the primary governing body---for some one thousand years. Even by the start of the Industrial Revolution Britain had already been in its current form of government for over 700 years.
3. Britain has a very strong and stable currency (the pound), allowing them to purchase imports cheaply from the rest of the world. Their central bank has never defaulted on debt in centuries, and thus has the highest level of credibility for borrowing; so they are essentially unconstrained in how much money they can borrow when they need it.
4. Britain has well-established property rights and relatively free markets. While they are certainly not wholly unregulated (and were considerably more tightly regulated in the 18th century than today), markets in Britain generally have been more limited and permissive in their regulations, allowing private innovation to flourish without excessive barriers or heavy-handed government intervention. Their court systems have a reliable record of establishing and enforcing clear property rights.
5. Britain has a very high level of education. The educational system in Britain has been one of the best in the world for centuries, especially at their very top universities such as Oxford and Cambridge (both of which were founded hundreds of years before the industrial revolution!). This high level of education allowed them to produce the large numbers of highly-qualified scientists and engineers necessary to establish an industrial economy.
6. Britain has enormous reserves of coal. Coal was the chief fuel of the industrial revolution, and Britain had at that time one of the largest proven reserves of coal in the world. This made coal cheap and easy to get, and thus made it much more profitable for businesses to industrialize.
Beyond that, it is difficult to say which of these factors was most important, and there are very likely other important factors as well.