The following sources between them permit the relatively rapid location of most lead mines in the UK save for ones that closed prior to the 1840s:
1. The British Geological Survey Mineral Statistics (R.Hunt, ed) published annually for 1854-1881 plus some earlier predecessors of the late 1840s (also R.Hunt. ed), and its successor the UK governmental Mineral Statistics published annually for 1882 to 1896, and its successor, Part 3: Output of the Annual Report of H.M. Chief Inspector of Mines published annually for 1897 to 1914 record the great majority of productive mines of all types, including lead though omit mines which closed prior to their coverage. These original annual volumes contain only rudimentary location data. The data has been republished with Ordnance Survey six-figure National Grid References by Burt, Waite and Burnley (eds) for all the major non-ferrous mining districts of England and Wales, with one or more pre-1974 counties (the 'historic counties') per reprint volume.
2. The British Geological Survey published 30-odd volumes of Special Reports on the Mineral Resources of Great Britain from the early 1900s onwards, including volumes on most non-ferrous mining fields of note. Details of the mines was substantially drawn from the Mineral Statistics; locations are given by latitude and longitiude. Most of the non-ferrous volumes were reprinted in the 1980s by Mining Facsimiles.
3. The Northern Mine Research Society's British Mining series of memoirs published in the 1970s Foster-Smiths seven part gazetteer of Welsh non-ferrous mines; this locates all lead mines of note and a very large number of lesser mines and trials and gives national grid references for them.
4. The Northern Mine Research Society's British Mining series of memoirs also provides coverage of some English and Scottish lead mining fields, for example a gazetteer volume of non ferrous mines of south west Scotland.
5. There is a voluminous literature on the Derbyshire or Peak District lead mining field which contains an especially large proportion of mines which closed prior to the Mineral Statistics commencing, including for example Rieuwerts' four volume recently published history which might double as a gazetteer.
Between the foregoing publications, a week's manual transfer of data to a GIS system would provide you with most of the data you are seeking.
Best wishes with your research.