There is a map, but it certainly does not show all boreholes.There is a map showing all boreholes / Wells. Attached to that is a box that shows how much water can be pumped from each site. It doesn't list who the licence holder is.
Two of the three I mentioned above were certainly done officially, one of which I had to fill records in for it to, originally, Yorkshire, Ouse and Hull River Authority, name changed a few times over the years. This was drilled after seeing a system at the Yorkshire Showground at Harrogate.The bgs maps show all registered ones, but I know of two not on the map as they, despite being over 50years old were never done officially, and several done to drain a quarry not listed as water abstracton but as boreholes.