See in particular episode 6 in the original 1978 series (just going by the summary on Wikipedia).
Europe's coal belt starts in Scotland, runs through England, into France (and a nubbin in northern Spain / Portugal), Germany, and Silesia.
Oddly enough, the first countries to industrialise were, in order, England (which wasn't busily falling to pieces and/or fighting off invaders), then (after they'd stopped falling to pieces and/or fighting off invaders) France and Germany. They remain the heart of the European economy, a century and a half later.
The third great set of coal deposits were in the United States, though that was a country that also had tremendous forests, more readily accessed (and frequently local to where energy was needed). Coal consumption didn't exceed wood as a fuel until the 1880s. The US also benefited from oil, and was the world's leading extractor of oil from the 1860s to the 1950s. Having first developed coal, iron, railroads, canals, and steamships, the US could usefully transport that oil from the remote rural regions in which it was found (Titusville, Pennsylvania, Ventura, California, Spindletop, Texas) to the urbanised regions (New York, Philadelphia, Boston) where it was used.
The bootstrapping of technology was itself a really interesting story -- gunpowder, metallurgy, iron, fuels, steel, electricity, and prime movers, most especially diesel and gas turbine engines. See Vaclav Smil (Energy in History) and Manfred Weissenbacher (Sources of Power) for more on this.
(The fourth coal belt is in China.)
Rome and the Mediterranian had a long history of deforestation, going to Egypt and Sumer. The first story, the Epic of Gilgamesh, can be read as a story of ecological limits and deforestation.
Roman heating systems, hypocausts, had voracious fuel appetites. I'm not finding a solid reference but believe one could consume a ton or more of wood daily. That was imported from distant locations.
Early industrial windmills and water wheels typically produced 10 - 20 kW of power, with perhaps a few thousands throughout Europe, for a total power capacity of a few tens of MW. The power availed by coal and oil is thousands and millions of times this.
U.S. woodfuel consumption wasn't sustainable, and hasn't increased from levels of the late 19th century.
Interestingly our roads were built with bicycles in mind:
https://www.theguardian.com/environment/bike-blog/2011/aug/1...
Many similar sources such as:
http://www.citylab.com/commute/2014/12/the-secret-history-of...
In fact, Dunlop invented the pneumatic tire for his son's tricycle and they were initially used for bicycles (https://en.m.wikipedia.org/wiki/John_Boyd_Dunlop#Pneumatic_t...)
As of the late 19th century, horses consumed about 25% of the grain production of the US. Much of that was to provide drayage of people and goods to and from railroad stations or train yards.
A horse was a major capital investment. And a donkey can't carry all that much weight -- a light adult, perhaps, but only just.
The US horse population in 1915 was 20 million, contrasting with about 100 million people. Keep in mind that most of those horses were in commercial use -- drayage, farm traction (a large combine would be drawn by 40 horses), etc.
Numbers for England/UK are harder to come by, but a Google Answers thread gives 3.3 million for late Victorian Britain, and 14 million in Europe in 1800, the latter against a human population of 203 million.
The typical person, or family, owned zero horses.
http://answers.google.com/answers/threadview?id=144565
http://www.geohive.com/earth/his_history1.aspx
Though you raise an interesting question: what was ownership of draught animals throughout time, and how did that compare with bicycle sales in, say, the US, England, France, and Germany from 1880 - 1920 or so. Keeping in mind that mass private automobile ownership wasn't really a thing until the 1950s, even in the US.
I also read a great theory once (but I can't find it again through google!) that the industrial revolution really required the invention of the cannon first. Building an efficient steam engine in roman times would have been incredibly expensive and dangerous, because of their primitive metal technology. The cannon created a tech race between nations to develop more/better/cheaper/lighter cannons. Which resulted in better metal working tech. Once you can make big pieces of metal that can withstand and direct the pressure created from explosions, steam engines aren't too far away.
But Heron's invention was still useful, and would have been the fastest moving thing ever built up to that time. Perhaps it could have been adapted to military applications, like flinging tons of rocks really fast at high speed?