I signed out and went to read again the info in the Wakefield Memorial page 213. He does list sources on this page and does explain the John Wakefield part of the family tradition here.
"The first official record of a Wakefield in Ireland, we find in the Rememberances of the Exchequer, Dublin: John Wakefield is mentioned under date 1637. (See Records of Dublin, p 610 published 1821-1825)
"In the Landed Gentry When Cromwell Came to Ireland, by John O'Hart, Dublin, 1884: among the enrollments of the adjudications in favor of the 1,649 officers, formerly designed the "49 lots," preserved in the office of the chief, John Wakefield is enrolled. these adjudications refer to the arrears of the commissioned officers who served Charles I before the 5th of June 1649, in the various wars of Ireland. The index locorum of these enrollments is given on pp. 638-647 of the Records of Ireland, above mentioned, (See 3d ed of O'Hart's Irish Pedigrees)
I have not found these records, have you?