Gruff Rhys is packing for a trip to Mexico. He crosses the Atlantic at a strange moment, suggests Hot Press. “We won’t be going anywhere near Trumpland. Maybe we’ll see it from the plane,” says the Super Furry Animals frontman in his treacly burr. “Fucking hell man… fucking hell… ”

Super Furry Animals are about to embark on the mother of all victory laps. The 20th anniversary of the Welsh psychedelic crew’s debut LP, Fuzzy Logic, recently passed so, starting in Mexico City, they are going on the road playing the album in its entirety. Just for laughs – and because one 40-minute record would make for rather a short set – they will also reprise 1997 follow-up Radiator (the tour hits Dublin on Thursday, December 1).

“The first album didn’t sound anything like we wanted it to,” says Rhys. “We went into a big flashy studio we didn’t know how to use. With the second one we went back to our producer’s house and had a smaller setup. It was easier to mess around and experiment.”

Super Furry Animals have, for the past two decades, reigned unchallenged as UK rock’s most endearing eccentrics. They’ve had straight up pop smashes (2001’s Rings Around The World was a top five hit in Britain), released a Welsh-language collection and, in the video to the 1999 single ‘Northern Lights’, celebrated the ancient Irish sport of road bowling. In the best sense, you never know what is coming next.

Their earliest initial incarnation was as Britpop party-crashers. These five friends from Pembrokeshire in south Wales were discovered by Alan McGee of Creation Records at a pub in Camden in 1995.

“We were over the moon to be signed to Creation,” says Rhys. “Growing up we’d been massive fans of all their bands: Primal Scream, My Bloody Valentine, Jesus and Mary Chain. It was like being in some strange dream for us all to meet those artists.”

McGee has been widely recognised as a visionary, albeit one who tended to fly by the seat of his pants. With the success of Oasis ushering in a period of unabashed bacchanalia at Creation, how did the Super Furries find the label to deal with?

“They were hands-on in that they were aggressive about putting the artist first,” says Rhys. “They had good advice. Mark Bowen, our A&R guy, would come into the studio with these obscure albums – all this American college rock for us to listen to.”

The Super Furries went mildly crazy, when they had Creation buy them a branded tank, which they drove around Glastonbury festival in 1996.

“It actually only cost about eight grand – plus another two for the paint job,” remembers Rhys. “At the time, a full page advert in the NME would have cost around 20K. We asked Creation would they mind if we didn’t have an advert but a tank instead. It was that kind of time – a lot of dreams were coming true.

“We caught the tail-end of the era when bands still sold records. Oasis sold a hell of a lot and financed ours – it was like being in some kind of betting syndicate. We as a five-piece won the pools and were able to quit our day jobs and go on the road.”

The cover of Fuzzy Logic featured Welsh marijuana trafficker Howard Marks in a variety of his disguises. Soon afterwards, Marks published his memoir, Mr Nice, and became a familiar figure on the spoken word circuit (and long-time friend of this magazine), prior to passing away in April.

“We’d written a song called ‘Hangin’ With Howard Marks’, that was all about things that were very unlikely to happen – such as hanging out with Howard Marks. Then he was on the front of the record and his autobiography came out. He proved to be extremely popular.

“We were happy about that because he represented a different side of Wales – we didn’t want to be dealing with rugby and leeks and all of those stereotypes. He was a very interesting counter-culture figure. He put Welsh to use in interesting ways because when he was overseas smuggling drugs nobody could understand it.”

To coincide with the tour, Fuzzy Logic has been reissued in the usual super-deluxe format. However, putting out a spruced-up version of the record was a challenge, as the band discovered when they went looking for the master tapes.

“Creation was sold to Sony who then merged with BMG,” explains Rhys. “Then the Monopolies and Mergers commission broke up Sony BMG and BMG took the Super Furries’ back catalogue. What we didn’t know is that it was transferred to a warehouse in California. There was a massive fire and when we got the tapes back they had water and smoke damage. In a funny way we were fortunate that the band’s name starts with the letter “S”. If it had been further up the alphabet it would have been destroyed.”

Rhys and the rest of the band grew up in the Welsh-language community in Pembrokeshire. The singer is fervently anti-Brexit and ahead of the vote released a ballad entitled ‘I Love EU’.

“Wales is polarised like anywhere else. In the Welsh speaking areas, the pro-EU vote was eighty or ninety per cent. Five years ago, a vote to leave the EU would have been unimaginable. Thanks to the media, we are living in a post-truth environment. With the austerity that’s been going on, people are frustrated.”

And yet this was also the year in which Wales came of age in the sporting sense at the European Championships. “It’s very schizophrenic,” he nods. “Thousands of people greeted the team on the streets when they came home. It’s been a strange several months – a time of highs and lows.”

Super Furry Animals perform Fuzzy Logic and Radiator at the Olympia Theatre, Dublin on December 1. Tickets are available here.