It wasn't the most auspicious of meetings: "I shook his hand after a concert like a sad fan-boy." Jonny Greenwood, Radiohead's creative catalyst, one of the world's great guitarists, and floppy-haired pin-up boy for the musically adventurous even in his early 40s, is talking about 78-year-old Polish classical composer Krzysztof Penderecki. For most of the musical world, it would be Greenwood who had the star quality rather than Poland's most eminent living composer – even if Penderecki did break creative barriers in the 1950s and 60s that are still rocking Greenwood's world. In fact, Greenwood's obsessive enthusiasm for Penderecki's music, especially his still radical early work, has brought the sounds of musical modernism to new audiences in ways Penderecki could only dream of.

Greenwood's fan-boyism has also resulted in a recent new work, 48 Responses to Polymorphia (the latter being Penderecki's 1961 composition), a new CD, and a live concert, in collaboration with Penderecki himself. But for all that to happen, this musical odd couple had to meet again. Greenwood travelled to Penderecki's home outside Krakow, with its hundreds of acres of arboretum, and this time, Penderecki knew who he was. Sort of. "I was trying hard not to be intimidated or overly starstruck," Greenwood says, "and he was trying very hard to put me at my ease, which made me even more anxious. I kind of wish he had been more foreboding, but he's just very friendly." Penderecki also had his preconceptions shattered. "I didn't expect to meet somebody from pop music who was really quite a normal person," Penderecki laughs. "He dresses very normal, he has dignity and very good manners." Had Penderecki heard any Radiohead? "I told my granddaughter, and she knew immediately who they were. She is 11, and she and my children gave me some discs to hear their music. I like it very much; it is very soft, very musical. And after that, I heard that Jonny was inspired by me in other pieces he has composed."

Since 2004, Greenwood has written for the London Sinfonietta, for the BBC Concert Orchestra, where he was composer in residence, and for the AUKSO Chamber Orchestra that tours to London later this month. And then there are his soundtracks. If you have seen Paul Thomas Anderson's There Will Be Blood, you have already become familiar with Greenwood – music from another of his Penderecki-inspired pieces, 2005's Popcorn Superhet Receiver, saturates his score for the movie.

Penderecki says that he has to thank Greenwood for introducing his music to a new generation of young people: when 48 Responses was premiered in Wroclaw last year, 9,000 young people packed the auditorium, "and they had never heard about this old guy Penderecki's music".

So what is it about Penderecki that Greenwood finds so inspiring? "His pieces make such wonderful sounds. And it is a beautiful experience to hear them live. Of all the composers whose music suffers from what recording does, Penderecki is one of the biggest casualties. I think a lot of people might think his work is stridently dissonant or painful on the ears. But because of the complexity of what's happening – particularly in pieces such as Threnody and Polymorphia, and how the sounds are bouncing around the concert hall, it becomes a very beautiful experience when you're there. It's not like listening to feedback, and it's not dissonant. It's something else. It's a celebration of so many people making music together and it's like – wow, you're watching that happen."

That is what the real lesson of Greenwood's work with orchestras has been. "The big message has been that I have fallen out of love with recordings of orchestras. Despite what hi-fi magazines tell you about how much money you should spend on your speakers, you're not there, you're not in the hall. Because when you are really there, and you hear an orchestra start up, it's like nothing else. That richness filling the room, that's my motivation right now. I'm really hung up on avoiding speakers and electricity."

Hang on a minute – Jonny Greenwood, programmer extraordinaire, guitar-obsessive, new-sound junkie, wants to give up electricity and electronics? "I know I'm being massively hypocritical, because yes, I spend hours and hours programming computers trying to create these things, and I still love doing that. But I keep coming back to orchestras and thinking, that's amazing. And if you've got all those musicians in the room, why would you want a laptop, or want it all coming out of speakers?"

There are ironies on ironies here. Penderecki's Polymorphia, composed in 1961, couldn't have been written without the Polish composer's experience of early electronics studios. And some of the detail of the piece is based on something that seems straight out of a sci-fi movie: Penderecki wired up psychiatric patients to encephalogram machines and played them an earlier piece of his, the Threnody for the Victims of Hiroshima, and then translated the graphs of their brain-waves as they reacted to the music into the textures of Polymorphia. Greenwood has his own lo-fi homage to that idea in his 48 Responses. Partly also in tribute to Penderecki's love of trees, Greenwood found an oak leaf in his garden, and transformed the contours of its veins and sinews into musical material. Fake Plastic Trees no more … "I hope he sees it as a gesture of affection," he says, "but it might be one of those things that looks better on paper. I only let that part play for about 30 seconds of the 20-minute piece."

Greenwood admits, "there is something retro about what I'm doing, but I also think there's something that is still exciting and relevant in writing for orchestras. It's funny, but to me, when you go to a concert hall and hear electronic pieces from the 60s, I think they sound really dated. But when an orchestra plays a piece from that period, and it's going to sound different every time, it's feels more modern to me. And that's why Penderecki's early music, and the whole thing of writing for orchestras, still feels very modern. If I think about music in the future, I imagine it often as not involving electricity, in some dystopian, post-apocalyptic future. And that's what I get from Penderecki: people making music by taking these instruments out of boxes and playing them. That's a very bizarre and modern thing."

Jonny Greenwood, saviour of the orchestra – why not?

All of this has an impact on Radiohead, too, with Greenwood's ceaseless quest to make the band's sonic palette as flexible as any orchestra. They are about to tour the US, which is the best time Greenwood finds to write his film scores and orchestral music, "instead of doing something healthy such as going to the gym or seeing exciting people. It's the perfect situation to work." He shows me a music notebook he's been filling with sketches for the new Paul Thomas Anderson movie he is scoring. "I've sort of learned grownup music handwriting. I used to colour in crotchets with my tongue out" – he mimes a pose of schoolboyish concentration – "but a few years ago I finally sped up."

But Greenwood doesn't need any false modesty when it comes to his classical pieces. His 48 Responses isn't just a good piece for a composer who is more used to the studio, it is a dazzlingly imaginative, gripping and novel work, full stop. Don't just take my word for it: Penderecki thinks so too: "None of what Jonny does is a copy of what I have done. Even his notation is different from mine. He does things that I haven't done, and has gone in a different direction using some elements of my music. He is very gifted. I like his music very much." Who's the fan-boy now?

Jonny Greenwood's album with Krzysztof Penderecki is released on Nonesuch on 12 March. Penderecki conducts his pieces from the album with the AUSKO Chamber Orchestra, and Marek Moś conducts Greenwood's works as part of the Kinoteka Polish Film Festival at the Barbican, London on 22 March.