Any removal of material from beneath a home, whether recent or historic, can influence the foundations and structure as a whole. The extent of any damage will depend on the age, extent and depth of the workings.
The first step in identifying the risk will generally be carried out by your solicitor with the land searches when you purchased the house. If you are uncertain you can write to the appropriate authority, which in most cases will be the Coal Board.
If you suspect that there is a problem with mining related subsidence then contact should be made with your insurance company. If there is found to be a problem with structural movement from this cause they will be able to advise accordingly.