But it's a modest lair to which I track him on the outskirts of Guildford: a plain bungalow, with a high-speed Audi sitting outside. Fast cars are his preferred mode of transport and his extracurricular passion: toy racers sit on the mantelpiece of the back room where he practises his art.
The room isn't large, and the piano - an 1890 Steinway - dwarfs everything else. Behind his head as he plays is a painting of sea and sky, a pale blue vagueness that seems designed to induce dreams. Above him are two photographs - a boldly smiling couple, and a Nijinsky boy-girl: his parents, and his violinist wife. There is also a framed letter in a vigorous, flowing hand from the great Ferruccio Busoni to his publisher. These are the household gods under whose gaze Demidenko labours six hours a day, or 12 if he's preparing something large, such as his celebrated tour of Western music at the Wigmore Hall.
I ask about his origins, and he produces a photo album in reply. Self, aged one, in his home village; father looking forceful in army uniform; self with parents and elder sisters all with the same broad features on the beach by the Sea of Azov. Who is that winsome little elf with her hair in a bow, posing balletically in a black tutu? "Me. At a fancy dress party."
When did he begin to play the piano? "My mother claims I started before I was steady on my legs. I'm not sure I believe that, but the piano was always exciting to me, and I had no trouble finding my way around it." His manner is quick and ironic; his intonation - despite his excellent English - indelibly Russian. He started at Moscow's formidable Gnessin Institute when he was six, and studied there - "under a wonderful teacher" - until he was 17. He went on to study at the Moscow Conservatoire, and stayed to teach.
"But at that age people come with fixed habits, and you can't change much. If you want to do something significant as a teacher, you must start with the little ones, as I did when I came to Britain." At Yehudi Menuhin's invitation, he became a tutor at the Menuhin School. What does he make of recent allegations that that institution subjects its pupils to inhuman pressure? "Inhuman pressure? Compared with the Gnessin, it's a holiday camp." He details all the things besides music that he and his friends had to study, including the history of the Communist Party and endless team sports.
Demidenko's tutor at the Gnessin was Anna Kantor, who has since won fame as the guru whom Evgeny Kissin drags around the globe. And he well remembers the three-year-old Kissin's audition at the school: "He was tense and wordless, but completely and entirely a genius. He played Rachmaninov's Second with his tiny little hands, and though he obviously couldn't play all the notes, he could pick them out individually for any given chord. That was a gift from God." Demidenko was one of the musicians who later induced an initially sceptical conductor and orchestra to accompany Kissin in Chopin's two concertos, for his public debut at the age of 12.
What is his view of the pianistic production line? Aren't too many being trained? He knits his brow, says he would hate to criticise his colleagues, looks embarrassed for a moment, then lets fly. "Unless the child was close to genius, I would strongly advise against their going into it. If you want to make money, there are far easier ways. Pianistic virtuosity is a form of Darwinism - natural selection, with the public as arbiter. It can lead to tragedy." He suggests that musical education, including the reading of scores, should become part of the universal curriculum, and that the army of disappointed virtuosos could be absorbed as teachers. "That might help prevent those broken lives."
He counts himself lucky to have trained under the best system of music education in the world, but one that is now in the past, with its leading lights either dead, retired or teaching abroad. "Life in Russia is now simply a struggle for survival. People are not interested in music. It takes generations to build up a tradition like the one we had but only a few years to destroy it." Last week, to his great delight, he was granted a British passport. Does he go back home to play? "No."
He looks back in gratitude to his privileged days in Moscow when Gilels and Richter were regularly performing there. But he is now exploring electronic music and unwinds at night by creating computer programs for his own compositions.
He plays me a recording of the Gershwin concert he gave with Izao Tomita in New York's Battery Park, with 100,000 people in the audience. "Synthesisers are actually a source of inspiration. They can give me sounds and colours I never heard before, which I can try to re-create on the piano." He is an ardent admirer of Peter Gabriel: "I know classical composers who would give half their lives for the ability to write melodies like his." So what does he think of classical music's contemporary greats?
Not much. "It may be a problem with my upbringing, but for me, music has to be emotional communication. If it is created cerebrally, it doesn't move me. I love Scriabin's music, but in his late pieces I feel he's playing with millions of shards of a broken mirror which he can't glue back together. I feel the same about Stravinsky and Prokofiev. There is a confidence, an integrity of thought and feeling in Romantic music, which is now lost for ever."
Demidenko seems a happy man, in the grip of a magnificent - and marketable - obsession. "Performing music is like a woman being pregnant. She can't be pregnant for three or four hours a day - it's everything to her, all the time. As a pianist, you've got to live music 24 hours a day, in traffic jams, on trains, even when you are sleeping, which is when you can sometimes solve musical problems. If I ever catch myself not thinking of my music, I'll change my profession."
n Nikolai Demidenko plays Prokofiev, 7.30 pm tonight, RFH, London SE1 (0171-960 4242). His CD, 'Nikolai Demidenko Live at the Wigmore Hall' is on Hyperion A667781/2. His next solo recital in London is at the Barbican on 11 Feb