1. John is the son of Elizabeth (Courtenay) Rogers [unknown confidence]
2. Elizabeth is the daughter of William Courtenay [unknown confidence]
3. William is the son of Philip Courtenay [unknown confidence]
4. Philip is the son of John Courtenay [unknown confidence]
5. John is the son of Philip (Courtenay) de Courtenay [unknown confidence]
6. Philip is the son of Margaret (Bohun) de Courtenay [unknown confidence]
7. Margaret is the daughter of Elizabeth (Plantagenet) de Bohun [confident]
8. Elizabeth is the daughter of Edward (Plantagenet) of England [confident]
I do not have access to Richardson book if John Rogers is not in it you would have to check the sources from Edward 1 to John Rogers to see if they are sound, not just some ancestry family tree or my heritage or Geni with no sources.
William Courtenay was an ancestor of the gateway Humphrey Davie, so the lines back from him are in the books. See here, if Google will cooperate
His best line is through "Elizabeth of England (dau. King Edward I)", commonly called Elizabeth of Rhuddlan.
William Courtenay's wife Margaret Bonville also has an Edward I line, on her mother's side.