The eldest s/o Jane and George WICKHAM is shown in NZ records as "Charles John" :
I had hoped there might be London baptism records for Charles and his brother Thomas.
Thomas I can't even see a birth registration for ?? ... and Charles John I found had been registered and baptised, but in the surname of DALE.
Hammersmith & Fulham > Shepherd's Bush - St. Stephen
DALE - Charles John Baptised : 24 August
1862Born : 12 August 1862
Parents:
Charles and [this part has been struck through]
Mother: Jane - single woman - residing at 21 Providence Place
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[Maybe the parents were a bit lax about registering births ?

Might account for George and Albert WICKHAM not showing on the NZ Birth index ? Of course it's worth checking the NZ birth microfiche record (available at larger libraries) too. ]