We may be researching the same family line.My G-Grandmother was Ellen Kershaw (b.1830)to William Kershaw and Prudence Bagnall (m.1813)who had several other children as well as Ellen - all births recorded in Manchester Cathderal Records.
Ellen married Thomas Couldrey, who was my G-Grandfather on my Father's side.I realise that there were a great many Kershaw in the area and perhaps your William may have been a cousin? nephew? to my William.
If you have any information which may be of mutual help, please get in touch with me here in Australia.