This line of the family, if Eliza's father is the Walter Honisett as suggested above, can be traced back to Peter Henesit who married Clemens Tole in Fletching, Sussex in 1569.  Peter was a hammerman in the iron industry of the Sussex weald.  By the middle of the 17th century the iron industry was in decline and the descendants of this family took up other occupations such as farming.  Some moved further afield in search of work and hence the incidence of Honeysett (and it's variants) families in other areas of the country today.

For lots of interesting Honeysett history and more ancestors read on.