Webb-1467 is highly unlikely to be his mother. His father is ostensibly called Richard, his mother has never been named.
From Oxford DNB (2008)
Cox, Richard (c. 1500–1581), bishop of Ely, and one of the most influential of the first generation of protestant reformers, was born at Whaddon in Buckinghamshire. Nothing conclusive is known about his parents, though the heralds record his father's name as Richard.
Even the descent of Sir Richard Cox 1st Baronet (cox-1919) who claimed he was of a Wiltshire family & great grandson of the Bishop has been questioned. The bishop is a can of worms.
Doubtless Cox-1190 is a product of the misinformation surrounding the bishop just added to another tree. (See also Webb-995.)