Gary Boyd Roberts' _RD 900_ contains a line for the Izard family of SC based on a recommendation from me.
A claim for the colonial connection occurs in _Survey of London: Volume 17, the Parish of St. Pancras, Part 1: the Village of Highgate_ (London County Council, London, 1936).
"This [cottage known as 'Andrew Marvell's cottage'] must have been the house assessed in the Hearth Tax Rolls in 1662–75 at seven hearths, and occupied by George Pryor, esquire, a London merchant. He acquired the southern portion of the Cholmeley estate (see p. 24) in 1641, when William Cholmeley, esquire, surrendered to him conditionally a messuage in Highgate with a barn, garden, orchard and field of four acres, and a yard adjoining the barn aforesaid, late in the tenure of Whorewood, and a barn and barnyard near adjacent, late in the tenure of Paker. The surrender became absolute in 1647, and the equity of redemption was finally released in 1658 by William Cholmeley, late of Highgate, esquire, only son of Edward Cholmeley, and grandchild and heir of William Cholmeley, late of Highgate, deceased. The estate included the four houses shown in the hearth tax return as occupied by George Pryor, Major Thomas Gunstone, Robert Lea and Paul Sindery (afterwards Mr. Felkin).
Dorothy, a daughter of George Pryor, was buried at Highgate on 29th August, 1644. Pryor was elected a Governor of the Grammar School on 5th June, 1658, and lived here until he died at the age of 80. (fn. 21) The three daughters of George Pryor were married to three brothers, viz. (1) Mary to Charles Izard of London, (2) Martha to Richard Izard, citizen and grocer of London, and (3) Elizabeth to Ralph Izard of London, grocer. Ralph Izard and Elizabeth had three sons, (1) Ralph Izard, whose wife was Dorothy, afterwards of Charlestown, South Carolina, (2) Benjamin Izard, whose wife was named Elizabeth, also later of Charlestown, and (3) George Izard of London, gentleman. The family was afterwards of considerable note in America. These three sisters had a brother, Charles Pryor of Edmonton, who married Mary, daughter of Jeremiah Richardson and widow of Thomas Hollier, who died on 23rd May, 1700, leaving a son George Pryor. Miss Mary Richardson, after she became Mrs. Pryor, inherited from her father in 1678, property on the opposite side of the road, in Hornsey, including Northgate House, No. 130, and Ivy House, No. 128, Highgate Hill, two beautiful houses which happily still remain. (fn. 22)
George Pryor's dwelling house passed under his will to his daughter, Martha, the wife of Richard Izard, citizen and grocer of London, by whom it was conveyed in 1681 to Ann Morgan, late of Southwark, widow, with remainder to Thomas and John, sons of Thomas Morgan, late citizen and grocer, deceased."
https://www.british-history.ac.uk/survey-london/vol17/pt1/pp7-18
Note the statement that the three Pryor daughters, Mary, Martha, and Elizabeth Pryor, had married respectively to three Izard brothers, Charles, Richard, and Ralph Izard of London. Also, the statement that two sons of Ralph and Elizabeth (Pryor) Izard were the Izards later in Charlestown, S.C.
With the knowledge that the Izard _vel_ Izode family also had a third alias, Shillingford, we can consult the 1634 Oxford Visitation pedigree of Shillingford (or Izard), which shows two of the sibling marriages (Ralph Izard m. Elizabeth Pryor, and Charles Izard m. Mary Pryor).
https://www.google.com/books/edition/Visitations_of_Oxfordshire_1574_1634_and/vE5bAAAAQAAJ?hl=en&gbpv=1&dq=pryor+highgate+izode&pg=PA30&printsec=frontcover
The wife of Edmund Shillingford alias Izode alias Izard, ancestral to these people, is shown as "Grisell, d. of ___ Newdigate, of Arbury, co. Warw., by ___, d. & coh. of Anthony Cave."
The Newdigate family, from which comes the royal descent, is taken back in _The visitation of the county of Warwick begun by Thomas May, Chester, and Gregory King, Rouge Dragon, in Hilary vacacon, 1682_, p. 34.
https://babel.hathitrust.org/cgi/pt?id=pst.000023822498&view=1up&seq=50&skin=2021&q1=shillingford
"Griswold [Newdigate], w: of ___ Izard alias Shillingford" was descended from families of Cave of Stamford, Cheney of Chesham Bois, and Neville of Rolleston.