ok so this is still still a long shot possible but is slightly more possible given the son's name of Alan
As the 1939 register said Joseph Davison was born 1917, I looked for him in 1921 living in Ashington
The 1921 required ages to be recorded in years and months.
Joseph's death registration in 1970 gave a birth date of 21 Mar 1917 and the 1921 census date was taken 19 June 1921, so he'd have been 4 years and 3 months old and there is one entry which matches that. The father on the return is not named Joseph.
BUT this child Joseph is listed as being an 'adopted son' (though they already have a son of that name,so it must have been confusing!)and the record says his mother is dead and the Davison family who had adopted him also had a son called Henry Drysdale Davison .
Henry Drysdale Davison married Mary F Lee Q1 1931 Morpeth
Harry is often used as an alternate for Henry and Molly for Mary
and searching FreeBMD births 1931-1950 surname Davison MMN Lee in Northumberland
shows Alan's older sister you mentioned born in 1931 and Alan in Q1 1943 Northumberland Central 10b 567
The 1939 register has Henry D and Mary F listed in Ashington as Davidson, plus one redacted entry which is likely to be their daughter
Boo
