The usual list of the vicars of Howden seems to come from Hutchinsons "History & Antiquities Of The County Palatine Of Durham"
I've gone back to the archives of Durham Priory to compile this list, which differs from Hutchinsons list to some extent.
Where a reason is shown, it's the reason the vicarage was vacant - so death means death of the previous vicar, resignation the resignation of the previous vicar.
Note 1 - there are no records of appointments to the Howden vicarage in the archive between 1322 and 1362.
The 1982 guidebook to Howden Minster, written by the then vicar, the Revd Barry Keaton, follows Hutchinson in listing John de Galmeton as vicar in 1341, followed by John Skarlet (no date). There may be more information in the Borthwick Institute.
There is a possibility that during this period the Canons appointed their own vicars - in 1350, Robert of Thirsk is instructed to present a vicar like the other prebendaries.
Note 2 - in the Calendar of the Register of Richard Scrope, Archbishop of York, there's a record of William Aghton as a vicar of a prebend in 1399. In the Durham archive, there's a letter from the Prior to William Aghton Vicar of Howden in 1401.
Note 3 - there's some confusion about the resignation of Thomas Litster. There's a record - in March 1418 - of Adam Walsh being appointed because Thomas Litster has resigned. However, in February 1419 there's a letter from John Aske (who was both the Bishop's steward in Howden and the Prior's steward in Hemingbrough) asking if Thomas Litster can exchange his vicarage of Howden for Adam Walsh's vicarage of Linton in Howden.
Note 4 - to add to the confusion, in the Calendar of Richard Scrope - link above - Thomas Litster exchanges his vicarage of Skelton in 1402 for the prebendal vicarage of Wistow - York Minster. However, according to the Durham archive, the vicar was called Luft, not Litster. I think the York reference is correct.
Note 5 - Barry Keaton's list has William de Riccall after Thomas Litster (with no dates) and no mention of William Wylkynson. The archive reports the death of William Rycall, vicar of Howden in 1450. William Wylkynson was a chantry priest in 1432, then vicar of Saltmarsh prebend in 1434. There is no other mention of William (de) Ryccall or Riccall in connection with Howden, so I think this is an error in the records, and William Wylkynson is correct.