This account is from the book entitled 'Woodgates of Stonewell Park and of Summerhill in Kent' by The Rev. Gordon Woodgate, M.A. and Giles Musgrave Gordon Woodgate, 1910 as a footnote to page 24.
"The Streatfeilds are one of the good old families of Kent and still retain all their original property at Chidingstone and the neighbourhood......... One of the family, the Rev. Thomas Streatfeild of Charts Edge, a man who has spent his life collecting materials for a history of Kent observes:- "Though I have failed to deduce the pedigree from an earlier source than temp. Henry VII (namely Robert Streatfeild, who married, as already mentioned, the sister of Sir John Rivers), the family appears to have been settled in and around Hever for several generations previously." He traces the name from the borough of Stretfield in Surrey, he thinks in Brede; though Mr R. Carter Smith deduced it from "Strete des felde". Perhaps it is unnecessary to go so far afield. It seems there was some land in Penshurst named Strattefiled; for in 1561 Willam Hart of Tonbridge sold to Robert Combridge of Penshurst, property called the Sandfields and four pieces of land called respectively the Garden, the Streake, Strattefield, and another. (Thorpe's collection, Society of Antiquaries)."
Woodgate goes on to list the branches of the family as:-
From Henry Streafeild of Chiddingstone, 1792.
From Richard Streafeild of Cransted.
The Streatfeilds of Westerham.
The Streatfeilds of Delaware (Brasted)
The Streatfeilds of Hever.
Current research shows that there were several Streatfield families active in Hever, Penshurst, Westerham and Leigh in the mid 1500's, it seems most likely that Robert Streatfeild came from Penshurst and may be a junior son of a family there.