I feel I might be able to assist you. Various family members have investigated the background of my father's side of the family (Walter George Phillips).
The name Billinghurst appears as a second name on a few occasions among ansestors. A family member visited the Mormon Church Family History Library at Greenwich and came across the following:
William Phillips married Sophia Otterway 25.12.1835 Merewoth Kent. William's father was Thomas Billinghurst Phillips, his mother was Maria Baker and the name Philadelphia appears as the third child of Thomas and Maria. Therefore William would have been her brother.
William and Sophia ultimately had 8 children and left for Australia on 27 November 1838 on the Lady Nugent. Their son Edmond John Phillips would have been my great grandfather.