Sorry to disappoint you both but the nursing home is no more. It was demolished in the 1980's and a small development of new houses was built on the site. I have spoken to a lady who lives in the new house that is built on the exact spot where she was born in the 1940's in Fairfield (as was I, as a matter of fact). It was run then by Doctors Duthie and Mcfarland. Dr Duthie lived in the house opposite on the righthand side going up Fairfield Road, and held his clinic in the outbuilding you can still see up the top of the drive.
I have tried to find out more about the home, but it seems to be shrouded in mystery, you can speak to Chesterfielders about it and most people had someone who had been in there, but no local autority know anything about it. There are certainly no records available anywhere. Strange?