« Reply #29 on: Saturday 11 March 23 03:16 GMT (UK) »
Found on FindMyPast site about 6 years ago in their collection Passenger Lists Leaving UK 1890-1960.
At the time I had a subscription to FindMyPast.
Also on the first page of this topic is a post which gives a link to the Family Search record for the family's emigration. The link doesn't work any more but if you go to the New Zealand passenger lists on FamilySearch, you'll be able to find it, albeit incorrectly spelt (as the rootschat member on the first page points out).
BLANCH London, Kent, Cumberland, Sunderland WALTON Cumberland, WILSON Cumberland, New Zealand, GRAHAM Cumbria/USA, DUNN Woolwich Kent, BLAKE Northumberland HENDERSON Renfrewshire PATERSON Argyllshire HALLAM Surrey BYRNE Dublin, BURNS Glasgow, DENSTON/BARBER Staff., WADMAN Somerset, DALE Middlesex, AIMERS Selkirkshire, BORTHWICK Berwickshire