Here is part of what I have.This is from "Your Family Tree" by David Starr Jordan and Sarah Louise Kimball, D. Appleton and Company, 1929.This starts from Henry Percy, 2nd Earl:
SIR HENRY PERCY, 2nd Earl of Northumberland, K.G. m. Eleanor, daughter of Sir Ralph Nevill, Earl of Westmoreland, K.G.[His second wife was Joan de Beaufort, granddaughter of Edward III.]
SIR HENRY PERCY, 3rd Earl of Northumberland, summoned to Parliament in right of his wife as Baron Poynings, FitzPayn, and Bryan, 1446, slain at the battle of Towton, March 29, 1461, and attainted after death; m. Elizabeth Poynings.
MARGARET PERCY, m. Sir William Gascoigne, Knight, of Gawthorpe, Yorkshire.
ELIZABETH GASCOIGNE, m. Sir George de Talboys, Knight, so nad heir of Gilbert, Baron de Talboys, of Kyme, d. 1566.
ANNE DE TALBOYS, m. Sir Edward Dymoke, of Scrivelsby, Lincolnshire, hereditary Champion of England, high sheriff of Lincolnshire, officiated as Champion at the coronations of Edward VI, Queen Mary, and Queen Elizabeth.
ARTHUR DYMOKE (brother of Frances [from whom George Washington is descended -- David], wife of Sir Thomas Windebank, of Haines Hill, Hurst arish, Berkshire, clerk of the signet to Queen Elizabeth and King James I, etc.)
EDWARD DYMOKE [This is often spelled "Dimmock," especially in American records; his middle name was Humphrey; born 1587 in Scivelsby, Lincolnshire -- David]
REV. THOMAS DIMMOCK, of Barnstable, Mass., freeman and Deputy, 1639; Lieutenant and drillmaster, 1643; ordained teaching elder of the church, August 7, 1650; nuncupative will probated 4 June, 1658, left all to his wife, for the children were hers as well as his. -- Pope's "Pioneers of Massachusetts".He m. Ann Hammond, granddaughter of Admiral Sir William Penn, father of William Penn, of Pennsylvania.
ENSIGN SHUBAEL DIMMOCK, m. Joanna Bursley, granddaughter of Rev. Joseph Hull.
Shubael Dimmock was Thankful Dimmock's father.She married Edward Waldo (1684 - 1767).
The above list starts with Henry Percy, 2nd Earl.He was born 3 Feb 1392 and died 22 May 1455.His mother was Elizabeth Mortimer, and his father was Henry "Hotspur" Percy, born 20 May 1364 and died 21 Jul 1403.His father was Henry Percy, 1st Earl of Northumberland, born 10 Nov 1341 and died 20 Feb 1408.He was the son of Henry de Percy, 3rd Lord Percy and Mary Plantagenet.Mary was the great-granddaughter of Henry III, King of England.
So Thankful Dimmock, wife of Edward Waldo, is the 13G-granddaughter of Henry III.