The most important of the iron machines was the steam engine. The looms and spindles of the mills were driven by steam. Steam engines pumped water from the mines, and hauled out men and coal. Railway trains were drawn by steam engines on wheels.
From 1700, steam engines were used to pump water out of mines. But they were slow and used a lot of coal. In the 1770s and 1780s, James Watt, a Scotsman, invented a much better engine. It needed less coal, and it could do more than just work a pump. Watt's engine could also turn a wheel, which meant that it could drive machines.
Watt's engines were made in Birmingham at Matthew Boulton's workshop. They were made one at a time at first - there were not enough skilled engineers to make the parts for more. By 1800 a few hundred were in use, in mines, cotton mills, and iron works.
The spread of steam power took place mainly after 1800. As more factories were built, more steam engines were needed. More workmen became skilled in making boilers and pistons. New firms followed Boulton's lead, supplying engines to all parts of Britain and selling them abroad.
Walter Robson: Britain 1750 – 1900; Oxford University Press, 1993/2002, page 16 f.