Bubblyrat, the tune that's used for To Be A Pilgrim is indeed a folk melody that was collected in Sussex, and had a previous and parallel life as The Blacksmith (and also in the related song "Our Captain Calle to Hands"). I don't know how old it is - there's no reason to think it's pre-Saxon, but it's certainly pre-English-Hymnal. There are quite a number of tunes of this sort, which have only been attached to hymns for a century or so. Another is "Be Thou My Vision", aka "Banks of the Bann".

I've heard it said that many of the (much older) Lutheran chorales and other Germanic hymn tunes were actually based on folk melodies. and certainly many British/European carols use traditional tunes that were originally secular dance tunes.

It's a fascinating subject and no doubt explored in other threads.
Marje