I can't see a birth in England for Ann/Anne/Annie Vernon Harper on freebmd. There is one for Annie Vernon in 1880 in Warrington, though. Given the gap between the other two daughters and Annie, could Annie be an adopted/foster daughter?
Given that one of the others listed on the 1881 census with the family was a 13 year old daughter named Anne it seems unlikely that Robert and Esther would give a second daughter the same name. With that in mind I think I found your Annie on the 1891 and 1901 census.
On the 1891 census for Gorton, Lancashire there is the following entry:
Geo Bigland, head, age: 24, occupation: police constable, born: Galgate, Lancashire
Anna Bigland, wife, age: 23, born: St. Helen, Lancashire
Margaret Bigland, daughter, age: 5 months, born: Gorton, Lancashire
Anne Vernon, cousin, age: 11, born: Warrington, Lancashire
(Source Citation: Class: RG12; Piece: 3176; Folio 33; Page 8; GSU roll: 6098286)
In the Free BMD there was a marriage registered in the 1st quarter of 1890 in Barton Upon Irwell, Lancashire for a George Bigland. The other names on the page were Annie Harper, Mary Clarke and Herbert Hancock. Given that the age and birth place for Ann Bigland matches that for Anne Harper on the 1881 census it looks pretty good that George Bigland married Annie Harper.
I also found Annie Vernon on the 1901 census in St. Helen, Lancashire listed in the household of George (Jr) and Francis Barton as follows:
Annie Vernon, barmaid, age: 23, occupation: barmaid, born: Warrington, Lancashire
(Source Citation: Class: RG13; Piece: 3519; Folio: 70; Page: 1)
I lost her after 1901 though.