Hi Alex,
A quick look at the 1851 census of Derbyshire/Staffordshire for people born in Cornwall brings up a few who were lead/coal miners or engineers. The Cornish had a lot of mining engineering experience which they exported all over the world ( USA and Australia for example) , so I expect quite a few travelled north looking for work. Also mines needed other trades such as stonemasons, carpenters etc.
If you are specifically interested in Lead mining the book by Raistrick is very good for general reading. I have Co. Durham lead miners in my ancestry and found the book very informative.
A History of Lead Mining in the Pennines
RAISTRICK, Arthur & JENNINGS, Bernard
Published by Davis Books (1983)
ISBN 10: 0946865000 ISBN 13: 9780946865000