Trish,
What a lot of wonderful information you have been given.
Do forget about the spelling! If you can even
think of a different spelling for a name, then it's more than likely that a given family will have been recorded under that variant at some stage! I think we'll all happily eat our hats

if the family which Kazza located is not yours!
For example, the census entry has little Percy WOOLLWRIGHT, age 1, born Wavertree.
What is surely his birth, in the Sept qtr 1879 in West Derby (which includes Wavertree) is listed on FreeBMD at:
http://freebmd.rootsweb.com/cgi/search.pl - but as Percy WOOLLRIGHT.
Have you looked at the IGI on FamilySearch (the site which Kazza mentioned) - at
http://www.familysearch.org/ ?
If you simply enter WOOLLRIGHT (any spelling) in the last name box and select British Isles as the region, you will note how very few entries there are.
Interestingly, your Ernest is one of them! This is not an entry extracted from Church Registers or Statutory Registers under the controlled extraction program of the Latter Day Saints but is an entry submitted by a member of the LDS.
This submitted entry in the IGI lists Ernest WOOLLRIGHT, born 1 Jan 1877, died 1958. His place of birth is given as Liverpool and his parents as John WOOLLRIGHT and Eliza Blackstone WAKEHAM.As you know Ernest's date and place of birth, you should be able to purchase a copy of his birth certificate which will give his parents' names.
A search on e.g. Google for the name (various spellings) brings up several hits.
Here's another mention of a Woollright & Co in Bold St - but as funeral directors?
http://www.encyclopedia-titanica.org/item.php/303.htmlAnd a Woollright attorney is mentioned on the Rootsweb Merseyside List in the 1843 Gore's Directory:
Knapper and Woollwright Attorneys Bretherton Blgs 10 n John St
I notice that Ggpa John's place of birth is given as Canterbury. Here's a mention of the name in Canterbury (Woollright & Parsons) in the 1840 Pigot's Directory for Kent
Click HereInterestingly, in the 1901 census at:
http://www.1901census.nationalarchives.gov.uk/a
free person search does not seem to find any of the persons listed in the 1881 census entry - perhaps the whole family migrated to NZ?
WOOLLWRIGHT - nil
WOOLLRIGHT - nil
WOOLWRIGHT - 9 results
WOOLRIGHT - 13 results
I see that the NZ online white pages has no listing for the first three spellings above and only 2 for WOOLRIGHT.
I think you will have a very fruitful time ahead in your research given that you are looking for such a very uncommon name.
Good Luck,
JAP