As you know, http://fmg.ac/Projects/MedLands/ENGLISH%20NOBILITY%20MEDIEVAL2.htm#... has nothing to say about his parents.
A Genealogical History of the dormant, abeyant, forfeited and extinct peerages of the British Empire, London, 1866, Burke, Sir Bernard. 543
The Complete Peerage, 1936 , Doubleday, H.A. & Lord Howard de Walden. XI 148
And for his daughter Alice Howard
~Genealogisches Handbuch des Adels, Fürstliche Häuser .1964
Is there any evidence this Suffolk man was a Justiciar of Ireland?
I think I have found an originating citation for the Peyton connection; it looks to have been particular editions of Burke's?
I've put back the connection. I'm unsure of the parents but I am sure of the brother
Sir John de Peyton of Peyton Hall in Boxford, who lived in the reign of Henry III. and was the ancestor of all the families of Peyton, had a younger son Robert, who was called De Ufford from his lordship of that name near Woodbridge in Suffolk, and was sent to Ireland as Justiciary in 1269* ' to settle and pacify Erin.'