Details of Arthur's birth are not known.

Arthur married Elizabeth Florence Greenhough in 1908 in Uttoxeter, Staffordshire.

He had the following children from his marriage to Elizabeth Florence Greenhough:

- George R Beckett	born in 1919 in Uttoxeter, Staffordshire.
- Arthur E Beckett	born in 1922 in Uttoxeter, Staffordshire.
- Eileen M Beckett	born in 1924 in Uttoxeter, Staffordshire.
- Mary E Beckett	born in 1927 in Uttoxeter, Staffordshire.

Details of Arthur's occupation are not known.