I think you are looking for Joshua Charles Tailby born 2nd Quarter 1875 at Blaby in Leicestershire GRO 7a 40
Married Lillian Sharps at Northwich, Cheshire 3rd Quarter 1901 GRO 8a 575 and appears on the 1911 census for Northwich.
I am assuming that Joshua Tailby, born Stockport 1st Quarter 1931, mother's maiden name Shorrock GRO 8a 121 is their grandson and a relative of yours.
Do you happen to know whether he is the Joshua Tailby who married Vera Rodgers in North East Cheshire, last Quarter 1956 GRO 10a 671? If so, do you know what happened to him? Is he still alive? I have a friend who is looking for information about him.