Hello Paul, Might have some help for you. 1871 census shows a John aged 1, born Walthamstow, Essex. Father - John Abraham Davey (35 born South Weald, Brentwood, Essex), Mother - Emma (31 born North Weald, Brentwood, Essex), other children Alice (9), Emily (5 born Chingford, Essex). John Abraham Davey listed as a gardener. They were living Churchfields, Walthamstow. Brentwood not that greater distance from Walthamstow.
Now - in the 1881 census,there is a John Davey born about 1872 who is a resident in Late Shorditch Industrial School, Brentwood, Essex. He is listed in a long line of children all coming from 'Hackney' - Hackney not far from Walthamstow - it could be wrong and whoever wrote the children down just said Hackney to them all. I wondered if John learnt his 'printer' trade at the industrial school.
The next finding of him is in the 1901 census with his wife Annie (29 - born in Yorkshire), children Mabel (3 born Pimlico, London) and John E (11 months - born Pimlico, London).
Hope this is of some help. John Abraham Davey vanishes for the 1881 census - may be he died - thats why John younger is in the school. There is an Emily - she is in service. Good luck in your searching.