As it happens, we played both Playford's Red House and Ty Coch Caerdydd at the pub last night.  The point of Anne Gilchrist's article referred to above was to illustrate the evolution of the tune from its earliest appearance in print (Playford, 1706) to, in one branch, the Welsh variant printed in Alawon Fy Ngwlad (c.1896) -where it has changed very little, though it is now a straight major rather than modal tune- and, in another, via Whaur would bonnie Annie (or, our Guidman) lie, to the tune to which Graves wrote John Peel.  A brief quote from Miss Gilchrist:

"For many years after Peel's death in 1854, Graves's song was only locally known, being 'droned over monotonously' to the third part (refrain) of the tune -to which it is still confined in popular use.  But about 1868, William Metcalfe of Carlisle" [the organist referred to earlier by Graham Pirt] "tracked down the original first strain, and published it (a good deal modernised) in that year.  In May, 1869, he was invited to sing his version at the annual dinner in London of the Cumberland Benevolent Institution... From having been current in local circles only, Metcalfe's... modernized form...gave it a fillip which ended in its becoming known not only in hunting circles but at social, festive and dance gatherings all over the world where the English tongue is spoken..."  -Journal of the English Folk Dance and Song Society, 1941.

The musical examples given by Miss Gilchrist (who knew what she was talking about) clearly illustrate the links.  Since she wrote, however, John Peel has largely reverted to being sung just to the tune of the chorus, so the connection between it and its relatives will not be so apparant to the ear.  It's still discernible there, though, if you listen for it.

Malcolm