William's birth in 1828 in the IGI (that should read christening) shows his mother as Evica WILLSON.
A search of that Harbury batch shows two other births with mother Evica (none for Avica - and none for Avice though, in my experience Avice is pronounced Avis):
Henry Thomas FINCH, bap 13 Apr 1834, Harbury, parents John FINCH and Evica
John FINCH, bap 15 May 1836, Harbury, parents John FINCH and Evica
Searching that batch for just father John FINCH also produces the following:
Hannah FINCH, bap 7 Apr 1839, Harbury, parents John FINCH and Abitha
Eliza. FINCH, bap 26 Dec 1841, d 17 Apr 1844, Harbury, parents John FINCH and Abitha
And then a search for a marriage between a John FINCH and a WILSON finds:
John FINCH m Avies WILSON, 1 Oct 1832, Coventry Warwickshire.
Hope this helps!
JAP