Good morning Annie,
Shakespeare and Ardwick rang some bells. Shakespeare St produced no hits, but somewhere at the back of my mind I remember attending a meeting so I tried Shakespeare Community Centre and found this
http://www.mancat.ac.uk/community/shakespeare.htmIt is located on Shakespeare Walk M13 which could just about be Ardwick. That area was pretty well knocked about in the 60\70's so perhaps there is an echo of an earlier street name there but I have no idea really

The link to streetmap.co.uk works so you can see it's proximity to Ardwick

And i've just found it on 1915 Godfrey map

It was in the location of the Shakespeare centre, so there is an echo of the name. It ran between Stockport Rd and Plymouth Grove. Do you want a scan of the map?
Have a great day
Cheers
Tony
