Hello Clair, how are you getting on with your Pickup Family Tree research?
I can confirm that Ernest Greensmith Pickup was the son of Walter Greensmith Pickup.
A little further research reveals that Walter Greensmith Pickup was born at Glossop, Derbyshire on 11/6/1884, the son of John Pickup and his wife Angelina (nee Greensmith). John's occupation at the time of Walter's birth was shown as "Calico Machine Printer". John and Angelina were married in the March quarter of 1883 in the Ashton (Under Lyne) Registration District. This is, as I surmised, how your Grandfather and Great Grandfather got their Greensmith names.
A check of the indexes of Registrations of Death reveals that Angelina's death was registered in the June quarter of 1937 at Dewsbury. Her age at death is shown as 78 years. Looking through the indexes of Registrations of Births I found Angelina Greensmith in the index for the June quarter of 1859 at Halifax.
John could be a little more difficult to find.
I hope that this is of help to you. If you would like further assistance, then please get in touch.