That isn't really the point, yes it was the 'age of steam' but in reality it made a few marginal mines profitable. There were no steam trains, no steam ships, no wide spread mechanisation.
Britain wasn't some backwater that was propelled ahead of spain due to accidentally discovering steam power. It was already a power in it own right, with trading networks and markets for these raw materials, that was the impetus for the development of steam.
https://en.wikipedia.org/wiki/Steam_power_during_the_Industr...
https://en.wikipedia.org/wiki/Thomas_Savery#Application_of_t...
Coal mining was a thosand times greater than metal mining by the late 18th / early 19th century:
Coal was so abundant in Britain that the supply could be stepped up to meet the rapidly rising demand. About 1770-1780 the annual output of coal was some 6.25 million long tons.
Versus:
Despite the collapse of the copper mining industry in 1866, the tin industry was still riding high producing 10,000 tons of tin a year - about half the world's production.
http://www.miningartifacts.org/English-Mines.html
Coal production 1700 - 1900:
1700 : 2.7 million tonnes
1750 : 4.7 million tonnes
1800 : 10 million tonnes
1850 : 50 million tonnes
1900 : 250 million tonnes
http://historylearning.com/great-britain-1700-to-1900/indrev...
More on copper:
During the middle of the 18th Century the quantity of British copper sold was over 700,000 tons.
https://www.copper.org/education/history/60centuries/raw_mat...
Plus that's 700,000 tons of copper, copper ore typically contains 2%? Copper, so your 700,000 tons of copper represents 35 million tons of ore. I'm undecided whether relative weight is even a good comparator. Sure value of output would be the best comparison?
You seem to be referencing Savery engines that weren't successful, whereas I'm referencing Newcomen engines that were. Can we agree that unsuccessful engines weren't a factor in Britain overtaking Spain?
