Ms Alison Maddock researched (2003) in the copy of the St Mary Church Calne parish register held at Trowbridge for records of Vines and possible variants. Some of the records are in Latin. 

Baptisms: 
9 February ?1558/9 (exact year uncertain), Robert Vine 
26 February 1563/4, Jelyan Vyne 
18 February 1564/5, Joan Vyne (in the Latin form Joanna) 
18 March 1582/3, Margery Vynar alias Woodrooffe, annotated with the letter B 
(probably means base-born, i.e. illegitimate) 
25 January 1584/5, Nathanall Vyner alias Hancocke, B (see above) 
26 September 1596, John son of John Vynar 
2 October 1602, Joyse daughter of Edward Vinarde alias Phillips 

Burials: 
4 November 1563, William Vyne 
5 June 1585, Thomas Vyner alias Phyllips 
30 October 1586, Nathanaell Vyner alias Hancock 
9 October 1592, Mawtilda wife of Robert Vynar alias Phylips 
7 February 1596/7, John son of John Vynar 
1597 (exact date to be checked), Robert Venar alias Phylips 
18 March 1604/5, Elyzabethe Veynarde 
27 July 1606, Edwarde Vinarde alias Phillipps 
27 June 1610, Joyce Vinarde alias Phillips 

Note that the Vynar(d)s later become Vennards, a local 
name in Calne. Dates with an oblique should be read as the second of the two 
years, in terms of the modern calendar. 

I found a set of apprenticeship records for Brinkworth at the WSRO (ref. 
1607/75). These are poor children apprenticed by the parish. The following was the 
earliest Vines to appear: 
8 October 1722, Daniel Vines, a poor child, apprenticed for 7 years (to the 
age of 24) by the churchwardens (one of whom was Benjamin Vines) and the 
Overseers, to Francis Pullen, blacksmith of Lineham.