He was educated at Cambridge and afterwards entered politics, becoming private secretary to the Prime Minister, Lord Derby, from 1852 to 1855, and sitting as member for Beverley from 1854 to 1857.
There is a tradition that on one occasion the abbot of Beverley, anxious to investigate the case for himself, visited Mother Shipton's cottage disguised, and that no sooner had he knocked than the old woman called out "Come in, Mr Abbot, for you are not so much disguised but the fox may be seen through the sheep's skin."
Most of the changes which he advocated were wise and have since been adopted; but the violence of Mackenzie's attacks roused great anger among the social and political set at York (Toronto), which was headed by John Beverley Robinson.
On the 24th of September 1361 the king gave Wykeham a prebend in Beverley Minster, on the 1st of October the prebend of Oxgate in St Paul's (which he exchanged for Tattenhall on the 10th of December), on the 22nd of November a prebend in St David's cathedral, on the 10th of December a prebend in Wherwell Abbey, Hants.
He built the monastic church of St Peter at Gloucester, and rebuilt a large part of that of St John at Beverley.