The DELEY/HOON children were born before Benjamin and Lydia married. Presumably the marriage was delayed until after the death of Benjamin's first wife, May (nee FOSTER) in the first quarter of 1961.

The GRO birth index shows Lydia's mother's maiden name as SMITH. There are two HOON/SMITH marriages around the right place and time, but the WWI records of George Henry HOON confirm that he was the father of a "Liddie" born 27 July 1911. His wife was Gertrude SMITH.

This should be enough to take you back to the 1911 census and beyond, but if you need any further help, do not hesitate to ask.