Thomas and Anne were my 8 x Great Grandparents, and although I have no further info on Thomas, (I wish I did) I have seen someones tree that gives Anne as daughter of Samuel Ware b.c. 1618, who was son of Robert Ware b.c. 1585, who was son of Augustine Ware b.c. 1560.Samuel was supposedly from Mamhead, Devon.Sadly I do not know the origins of this info, so cannot trust how reliable it is.
Any other info on the Underhays would be greatly appreciated, as my research is purely internet based and therefore very restricted.