Under other circumstances they could have continued down the same path they'd set out on for Unhalfbricking, a couple of Dylan covers, originals from Sandy Denny and Thompson and some of the traditional material that was being unearthed by bassist Ashley Hutchings, but Big Pink effectively took the Dylan covers factor out of things.
The songs on the Publishers Demo, as redone by The Band were too distinctively American to fit in with the English-oriented material from other sources. At the same time, the timeless sound that characterized Big Pink, which had nothing in it that said Hey, this is 1968, the tightly arranged ensemble playing, the interplay of three fine but quite distinctive voices pointed towards a possible new direction.
So first Liege & Lief and then the Sandy Denny-less Full House were drawn entirely from the English folk tradition and the Dave Swarbrick/Richard Thompson compositions that were aimed to fit squarely inside the same territory. Once Sandy Denny left, there was an arguable Band influence in the vocal interplay between Thompson, Swarbrick and rhythm guitarist Simon Nicol, and within the communal dwelling that housed the Full House era Fairport, Music From Big Pink was, by all accounts, on almost continuous high rotation.
So how, you may wonder, did this reinterpretation of English traditional music translate into the Latin-infused rock of Los Lobos. Quite simple. David Hidalgo is quite definite. Hearing the Fairport take on the English tradition, Hidalgo, Cesar Rosas and friends realized that they could do something similar with their own Mexican traditions.
At the same time as Fairport were delving back into the musical past of the British Isles, the Old Weird America aspect of The Basement Tapes kicked in big time. Now, when you're talking old and weird, the Stateside thing only goes back a couple of centuries. It incorporates odds and ends that were brought to the mix from all sorts of other traditions, but you're still only really going back to the seventeenth century.
You want old and weird? Check out some of those odd local British rituals that date back to pre-Medieval days, an indeterminate past that offered a number of avenues to explore in the search for something interesting in a contemporary sense.