Leis a, are you familiar with the new GRO Index?. It gives all death records from 1837 to 1915 and crucially gives age at death.
It is free to use on line. You need to register but no payment is required.
dave
If you use Free BMD and search for George Barnsley deaths between 1890 and 1980 and specify Sheffield and Ecclesall Bierlow you get a reasonably short list. In that list the most likely is George Barnsley died Sheffield age 60 in 1949.
Dave
Re the death in 1949, that Dave has found for you. The burial is on
this site. There are other 'Barnsley's' in the same grave and they
might tell you whether this is the right George.
Their is a death registration for William Barnsley, Q2 1891 in Sheffield.
His age is given as 39 years.
On the 15 March 1892 at St. George's there is a marriage for
Emma Barnsley, 27yrs, Widow, 14 Allen St, father - William Stevenson.
Patrick Hayes, 41yrs, Widower, 14 Allen St, forger, father - Dennis Hayes.
1901 census - 55 Pye Bank, Sheffield.
Emma Hayes, head, mar, 35yrs, dress maker.
Annie Barnsley, dau, 14, tailoress.
George Barnsley, son, 11yrs.
Harry Hayes, son, 8yrs.
Nellie Hayes, dau, 6yrs. All born Sheffield.
By 1911, the family are at 11court 4house, Fowler St, Sheffield.
Emma Hayes, head, widow, aged 46yrs, dressmaker.
Son Harry Hayes aged 18, dau Nelly Hayes aged 16 and
dau Annie Barnsley aged 24, tailoress trowser (sic) maker.
All born Walkley, Sheffield.
Emma is on the 1939 register and still living at Fowler Street.
Her date of birth is 12 Oct 1864.
Emma Hayes, death registration, Q2 1946, Sheffield, aged 81yrs.