I have just eliminated this as I have found the family in 1881 without Harold but will post the information anyway. 1881-RG9/4590 f8 p10 in case anyone else was looking at following the same route.
Looking at English census for surname Rushton in Pembroke, Wales there is just this one.
1871 Pembroke
Staying with her parents Samuel & Sarah Kingdom is Ann Rushton age 27 (1844) and her children Charles age 2 born Jamaica, West Indies and Elizabeth age 3 months born Nova Scotia.
Annie Kingdom married Charles Rushton in 1863, Pembroke RD
Could this be Harolds mother and siblings with children being born abroad.
The British armed forces birth registration index has Charles S Rushton born 1868 - regiment of father 84th.
Other Rushton births listed with same regiment
Sarah A 1864 Tenby
Anne M 1866 Valetta
Elizabeth 1870 Nova Scotia
Samuel 1872 Curragh