A native of the diocese of Dublin, Ireland, Norreys made a successful career for himself in the church and Oxford University.
He was later successively canon, prebendary and Dean of St Patrick's Cathedral, Dublin, occupying the latter post by 1457.
His controversies covered matters that had previously concerned his fellow Irishmen, Richard FitzRalph, Henry Crumpe and Dr. John Whitehead.
In 1437 he appeared before the papal judge-delegate and the Bishop of Bath & Wells because of attacks he made against the friars during his university lectures.
Norreys wrote sermons, a tract called 'Declamationes', a book of scriptural commentary and the Contra mendicitatem validam.