May I make the following suggestions :- a) Lorraine, if you don't know where in England William was born in August 1837 I suggest you first look in the St Catherines Index (a.k.a. the the General Register of Births) which commenced in July the same year and (despite its flaws) was set up as a national index of births. This may give you some reasonably firm evidence from which to continue your research. My own knowledge of the Blackett's (my mother's family) indicates they were mainly, but not solely, based in the counties of Durham and Northumberland in north-east England. Otherwise I would concentrate on trying to establish how and when he emigrated to NZ and what information can be gleaned from any surviving passenger lists. If you have not already done so I suggest you locate of copy of the book 'My Name is Blacket' by Nick Vine Hall ISBN 0 9597208 0. Which contains a lot of information on the origins of the Blacke(t)t family, several family charts, including details of some Blacketts who emigrated to New Zealand & Australia.
b) Dave, for plans and hopefully pictures of Wylam have you tried the Blackett estate papers in the Northumberland Record Office, Gosforth branch.