In Oct 2020, Gay Brennan established that the Wyndhams are not ancestors of the Newmans as used to be thought. See note on Dinah Wyndam's page.

Lady Margaret's brother was Thomas Howard 2nd Duke of Norfolk; two of his granddaughters, Catherine Howard (via his son, Edmund Howard), and Anne Boleyn (via his daughter Elizabeth Howard), where two of the six wives of Henry VIII.

Sources: Hand-written notes from an unknown source passed down from Harold Ernest Montague Newman
Website: http://www.bellucci.com/melonbel/genealogy/royalmatilda.html
Website: http://www.geocities.com/cromerhistory/wyndham_tree.htm

Earlier notes from Jerry Gandolfo:

Sir John Wyndham:
Born: 1450 in Felbrigg, Norfolk, England, of Crowthrope and Felbrigg,.
Died: 1503, beheaded in the Tower of London; buried in Austin Friers Church, London, England.
Father: John Wyndham (of Crownthrope, and of Felbrigg, Norfolk, which he later purchased of the trustees of Sir John Felbrigg, Knight of the Garter. This John Wyndham, in the 38th Henry VI, was one of the knights for Norfolk, and other accomplices of the Duke of York, were attainted of high treason.
Mother: Margery (Marjorie) Clifton (married in 1440, widow of 8th Lord of Hastings and daughter of Sir Robert Clifton, of Bokenham Castle, Norfolk.
Married: Margaret Howard, daughter of John Howard, 1st Duke of Norfolk and Catherine Moleyns
Children: Sir Thomas Wyndham, Ann Wyndham (married Geoffrey Radclyffe of Farmeston)
Note: Was at the Battle of Stoke, 1487, against the Earl of Lincoln, Lambert Simnel, and their adherents, and was knighted immediately after the victory. Afterwards was engaged in the interest of the House of York, was convicted of high treason, and was beheaded May 6, 1503

Source:
Website: http://www.bellucci.com/melonbel/genealogy/royalmatilda.html
Burke's , The Landed Gentry