Have found a probate record and all the details seem to fit except for one - they had a son.
John Edmund Kershaw aged 71 of 687 Rochdale Road, Royton, Lancashire died 26/7/1947. Probate Manchester 14 October to Sarah Kershaw, widow and Edward Kershaw, mechanical engineer.
According to marriages John Edmund Kershaw married a Sarah Heywood bc.1875 Failsworth in Jun.qtr.1900 Oldham - their son Edward b.Dec.qtr.1902 Oldham.
Looked through probates as one would think that someone employed by a bank would leave a will. His age seems to fit, lived Rochdale Road, had a wife Sarah and both bc.1875/6. The Edward listed must be their son as shown on census - but you say they didn't have any children??
Annette