A two-night preview at 2016's Edinburgh International Festival aside, Sigur Rós' epic 18-month world tour finally arrives in the UK for an extended stay this week. For a band currently creating their eighth album in 20 years – the follow-up to 2013's Kveikur – this tour is all about doing things differently. They have a newly designed stage set, for a start, but also a newly restructured three-piece line-up.

When keyboard player Kjartan Sveinsson left the Icelandic band just prior to Kveikur's release, he was initially replaced by two session players. This time, however, singer and guitarist Jónsi Birgisson, bassist Georg Hólm and drummer Orri Páll Dýrason are playing their typically expansive sound by themselves. 'We feel more exposed, and we have a lot more to do,' says Dýrason, now based in London, of the new arrangement.

'You know, we've been taken out of our comfort zone a little bit,' he continues. 'I had to learn to play the piano. Even though it's really nice for us to have other instruments around us, it's easy to get lost in that big group. It's been really good for us, to push ourselves a little bit, but we've had to rehearse a lot. I think it's been alright, though – it's a little worse, but we did it!'

Asked to describe the stage design for those who haven't seen it, Dýrason struggles to put it into words, which is surely a good sign. He does reveal an unlikely influence, however. 'We have three screens which split up the stage – there are lots of smoke and mirrors, you could say. Like our music, we're trying to create a sense of emotion, and people are coming to our show not to listen to an album, I guess. I like seeing a visually good live show. For instance, I've seen two Rammstein [the German metal band] shows and it's one of the best live shows I've seen, it's amazing. But I'm not always putting Rammstein on the record player at home.'

Despite all the time on the road, the trio have been writing songs, and Dýrason hopes a final recording session around February might prepare the new record for a release next summer. 'We've completed a few songs,' he says. 'They're kind of all over the place (in terms of mood). Kveikur was dark, and these are a little bit more happy, I think.' This time they've been working with producer John Congleton, whose lengthy credits include Laurie Anderson and Franz Ferdinand. 'I love to work with him, he's super-talented, quick and a good guy to have around. The sound is good, and you don't really have to fix much.'

At this stage in a lengthy career, and with the recent enforced line-up changes, it seems fair to wonder how Sigur Rós keep a sound which was always fiercely unique – particularly Jónsi's spectral choirboy vocals – new and interesting. 'Most of the time it comes from new equipment and instruments,' says Dýrason. 'It's very easy to get stuck in the same place if you only have the same ones all the time, so if you push yourself towards learning new instruments or software, something fresh will come out of that. Like, I recently bought a midi saxophone, so I can connect it to my computer and play choir samples alongside it. I've never played saxophone, I don't know the finger positions, but good music has already come out of it.'

Perhaps it's this sense of experimentalism which made the unusual move of appearing in Game of Thrones in 2014 – they played at sadist King Joffrey's wedding – such a natural move. 'It was great,' says Dýrason. 'It was a really short scene, but we were three days in Dubrovnic, in stupid costumes and hanging onto the actors. Although I'm a musician, and for me there was too much waiting around and drinking coffee, chain-smoking cigarettes. But it was great.' At least people mostly seemed to like it, unlike Ed Sheeran's recent, audience-splitting cameo. 'I haven't seen that episode,' he says. 'But whatever you do, there's going to be a bunch of people who hate it.'

Earlier he mentioned Sigur Rós' new music being more upbeat, possibly going against the grain of the times, although he has no idea where such optimism comes from. 'I guess it's just the headspace we're in,' he says. We've been writing these songs over a long period of time, almost two years, and the emotions are very different, kind of all over the place. Whereas Kveikur was written in really short bursts, this one has taken a longer time. We'll see what happens when we get together for the next writing session, but maybe the world needs something happy? Maybe we all need some positive things?'

Sigur Rós tour the UK from Sat 16 Sep–Mon 25 Sep.