Ken moxon was adopted or fostered by Bartha Barker.
She also adopted Elsie Barker (later Crawforth).
He would have been a step-brother to Thirza Harsley.
The only Ken Moxon in the 1911 census
was born in Ely, Cambridgeshire in 1909,
to what seems like a stable family.
Is this a likely possibility? It does seem an unusual name.