Jonas Kaufmann, though now a 46-year-old with a greying beard, is absurdly handsome. Not quite as gorgeous in the flesh as he is in the moody cover shots that accompany his new Puccini CD, but unquestionably a bit of a looker, with taut frame and perfect cheekbones. It is his blessing and his curse.

When I see him at La Scala in one of those invariably unfulfilling concerts – Puccini arias interspersed with orchestral interludes – I wonder about all the adulation. Is the lady in the third row who is becoming borderline hysterical hailing the great artist or lusting after one of opera’s rare sex symbols?

The “greatest living tenor” hype, the emphasis on his physical attributes, the internet rumours (emphatically denied) of a liaison with Madonna following the breakup of his marriage last year, all obscure the more banal truth that he is a singer with a deep commitment to opera, to the grind of living, breathing stage performances. These concerts to promote his new disc are the exception, not the rule. He describes opera – the real thing, not just the bleeding chunks – as a “virus”, and is determined to inject it into our bloodstream.

“Anyone who calls himself an opera singer is going to spend most of his time on stage,” he says. “It’s not only that I like the opera house so much and would miss it, it’s also a question of credibility. If you call yourself an opera singer but only do it in concert, there’s something wrong.”

Jonas Kaufmann, far right, in Andrea Chenier at the Royal Opera House.

Kaufmann’s seriousness is splendidly Germanic. For all the superstar trappings, he is a regular guy trying to sustain a career that doesn’t get overwhelmed by a Three Tenors-style bandwagon.

Not that a phenomenon on quite that scale would be possible now. “Those times are over,” he says. “It’s gone.” He admits the money in classical music back in the 1980s and early 90s would have been nice, but mostly he is content that he can have a varied operatic career without being chained completely to a marketing juggernaut. He has just one regret about the regression since the heady days of Pavarotti mania. “The only thing,” he says, “is that sometimes I wish people would realise how important opera is.”

Growing up in Munich in a musical family which had fled East Germany in the 1960s, he took the centrality of classical music for granted and loved to sing in choirs. Indeed, at first he avoided studying to be a professional singer because he worried the joy would be lost. When Kaufmann appeared on Desert Island Discs earlier this year, you could hear the pain he felt on being allowed to play only two minutes of each of his chosen recordings. To him, this was sacrilege.

His father worked in insurance, his mother was a teacher, and, initially, instead of singing, he intended to do a mathematics degree at university. But he quickly switched to musical numbers and, after studying in Munich, began to build a career. Then, in his mid-20s, he suffered a vocal crisis. “I had a very light, white instrument,” he tells me. “I tried to be bright and very flexible with a very high-sitting tessitura [vocal range]. That’s the way I was trained to sing, but I never had a reliable instrument. It was always very fragile, and every little thing immediately ended in cancellation.”

He had to start again from scratch and find his real voice, and it was working with the American singing teacher Michael Rhodes that eventually unlocked his dark, baritonal tenor. “He showed me a different way of singing,” says Kaufmann. “At first, it was very difficult and it had many downsides, but I knew even then that this was the right way because I could sing on and on and would never get tired. This was a sensation I’d never had before, so I stuck with it and refined it. It was like learning to drive a second time. That was the beginning of the real career.”

For some, the darkness of his voice will never provide the visceral thrill of a Pavarotti, but Kaufmann says many tenor careers have foundered on attempts to copy Pavarotti. “He was unique. He was a machine. He had a technique of his own and a voice of his own.” He prefers to compare himself with Franco Corelli, a much-admired Italian tenor of the 1950s and 60s. “At the beginning, the darkness [in my voice] was controversial,” he says. “People would say: ‘You are wrong for this repertoire, you shouldn’t do it.’ But somehow more and more it got accepted.”

Kristine Opolais and Jonas Kaufmann in Manon Lescaut at the Royal Opera House.

Kaufmann’s repertoire is unusually wide – in 2013, the bicentenary year for both Verdi and Wagner, he was one of the few singers in constant demand for both. “If you do only one part, it’s boring and also dangerous for your voice,” he says. There are always new peaks to climb. He recognises he is now at a crucial stage in his career – “everybody says the 40s are the prime years for a tenor” – and the next few years will see him take on a range of new roles: Otello at Covent Garden in 2017, Calaf in Turandot, Walther in Die Meistersinger, Tristan, and perhaps even Siegfried in the Ring, though it is likely to be a more lyrical, smaller-boned Siegfried than most. That would be enough for several careers.

He dislikes tying himself down five years ahead, except in his home town of Munich, where he sings every year and is already in discussion about roles in 2020, and at the Met in New York and Covent Garden, where he has strong attachments and which insist on long-range planning. Kaufmann says he doesn’t know exactly what he wants to sing or do that far ahead, so keeps as much flexibility in his schedule as possible, happy to make role debuts in revivals if that means he can slot them in at shorter notice.

He is very much his own man, not least in the way he has paced his career. “I always thought, ‘I’ll do it a little slower than others’. I was convinced there would be another chance. There is no need to grab every opportunity that comes up if you’re not well prepared. If you make a bunch of wrong decisions, this can ruin a career. This is something that is very difficult to teach young singers, because you cannot just tell them ‘Don’t take your chances’. That would be wrong. You need to trust your instincts.”

Kaufmann also dislikes the fact that he is expected to go on stage when he is unwell. He has said in the past that every time he sings someone in the audience will be recording it, it’ll be up on YouTube within hours, and a bad performance will stick to him. He contrasts the criticism heaped on singers who cancel with the latitude given to footballers. “If football players are injured, or have problems, or can only play half the game because they are not fresh enough, everybody says ‘Ah the poor guy’. They don’t say ‘Bastard! Why didn’t you warm up properly?’”

One date he will certainly show up for is the Last Night of the Proms next month, where he will be the first German to give the time-honoured rendition of “Rule, Britannia!” as the evening roars to its climax. “I feel like an ambassador,” he says with a wonderfully deep, stagey laugh. “I remember when I saw it on telly many years ago when I was 12 or 13, I couldn’t believe it was a classical concert. ‘What is that?’ I wondered. There are people cheering and waving flags, but still there is classical music. That’s the dream come true. That’s how we want people to react to classical music.” I suggest he sing a verse of “Rule, Britannia!” in German – might that be possible? “You tell me,” he says, intrigued by the idea. I claim credit for this if it does indeed come to pass.

His media-anointed status as the “world’s greatest tenor” gives him another ambassadorial role he feels he has to fulfil. “I have to be very careful,” he says. “If I bump into some fans on the street, I cannot just be rude and run away. Sometimes you want to go ‘Oh c’mon, can I have one free moment please?’ But it’s so precious and we need everybody. I want people to be able to enjoy live classical music 100 years from now.”

The burdens of fame and constantly being away from home contributed to the breakup of his marriage with mezzo-soprano Margarete Joswig, with whom he has three children. “I don’t know whether things would have worked out differently if we had had more time, but I believe they would,” he says. “Everything is on hold and every plan is postponed because you’re on tour all the time, and when you are there, the moments are too precious to spoil with the discussions that you need to have.”

If the 40s are the key time for a tenor, it tends to get harder once you enter your 50s. How long can he go on? “We don’t know how far it goes,” he says. “Not everyone sings into their 70s like Plácido [Domingo] does.” The truth is he doesn’t know where his career will take him. Despite his aptitude for mathematics, he insists everything he does is born of love, not calculation.

• The Last Night of the Proms is on BBC1, BBC2 and BBC Radio 3 on 12 September. The Puccini Album is released on 14 September and the recording of Aida on 2 October. A film of the La Scala concert will be presented by Arts Alliance in UK cinemas on 17 November.