I believe I've found William Henry Howard in England with his parents. It seems they are Charles Howard and Jane Watson (Chenoweth) Howard (I think their daughter married a Felton). What bothered me about connecting them at first was that Charles Howard and Jane Watson Chenowith didn't marry until 1854 (after already having 3 children). Also that Jane wasn't baptized until 1840. So she may have been baptized when she was in her teens (this is all according to records I found on Ancestry).
I found William with them in the 1851 England census. But because their marriage didn't take place until 1854. I thought perhaps the Jane Ann Howard in the census might be a first wife to Charles and the actual mother of William (who may have died) But I didn't find any records to support this, so she most likely is Williams mother.
I did find them on the passenger list going to New Zealand in 1859. It matches with the 1851 census plus the birth of Williams sister Francis in 1854. Also there are records for at least the five I mentioned in New Zealand cemetery records.
Charles' parents are James and Sarah Howard. Jane Ann Watson's parents are Richard and Ann (Watson) Chenoweth (I think).
I am including the passenger list, 1851 census and marriage record here. The other records are from Ancestry. In the case you don't have access, I can provide them to you for their profiles.
"New Zealand, Archives New Zealand, Passenger Lists, 1839-1973," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:FSBC-L3R : 12 December 2014), William Howard, 14 May 1859; citing , Archives New Zealand, Wellington; FHL microfilm 004411486.
"England and Wales Census, 1851," database with images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/SGPV-KW3 : 24 July 2016), William Howard in household of Charles G Howard, Wheathamstead, Hertfordshire, England; citing Wheathamstead, Hertfordshire, England, p. 15, from "1851 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives of the UK, Kew, Surrey.
||Jane Walton Chenoweth
[Jane Watson Chenoweth]
||18 May 1854|