It's generally accepted that the stories of fairies tied to specific locations across the UK and Ireland is due to the presence of magic mushrooms growing relatively close by.
The British isles do not have old mushroom foraging traditions (in particular, what mushroom foraging traditions there are, are younger than fairy stories). Without some solid oral tradition, going around sampling mushrooms looking for a high is very risky.
Even if there was a tradition, why would they be limited to only where particular mushrooms grew? They would surely be picked and transported then. For that matter, don't hallucinogenic mushroom varieties grow all over the British isles? Many mushrooms aren't very picky about climate.
In short I don't believe this at all.
The main point of the article is that they're psychedelic, but don't contain psilocybin as the active molecule.
In earlier centuries it doesn't seem unreasonable to allow the possibility of the mushroom ingester to describe their experience as visiting the fae realm, whether in the UK or otherwise - as an accidental occurence I don't know how else people from the past would be able to explain what they perceived to others?
Eating mushrooms without knowledge will kill you. Cultures either don't eat mushrooms, or they develop knowledge of what mushrooms are safe to eat and which ones kill you - or make you see elves. There's no world where people see elves but don't connect it to the mushrooms they ate 15 minutes ago. It's also not very plausible that they as a culture stopped going on elf trips, but remembered the elves and forgot what made you see them. In short there's just so many ways this is a bad theory.