The director was often taken aback by the intensity of Babyshambles-mania, but also impressed by the singer's ability to take it in his stride. "On the one hand, he really, really enjoys it, and on the other he also finds it really, really irksome," Pomphrey says during a break from editing.
"The problem is that it's there 24 hours a day. Pete does get hounded. One night, we were leaving by the back door of a boozer and a tabloid photographer was just waiting there for us. We tried to get Pete into the van, but the photographer still managed to get his pictures.
"But all this attention is not getting to him. He's quite thick-skinned, and he copes. Pete is intelligent enough to understand the folly of tabloid fame."
Doherty also appears capable of handling the sometimes obsessive devotion of his young fans. "For his fans, Pete expresses a romantic disenchantment with society," Pomphrey says. "To them, he's utterly adorable. I've seen him surrounded by a million fans, but I've never heard one ask, 'Where do you get drugs?' I've heard thousands ask him about his music."
In Pomphrey's fly-on-the-dressing-room-wall documentary, Who the F*** Is Pete Doherty?, to be broadcast on Sunday, the former Libertine gives some indication of how it feels to be under the unremitting scrutiny of the tabloid press. He shakes his head ruefully and sighs: "It is very dangerous for that thunderbolt of attention to come upon you."
Only last week, that thunderbolt of attention crashed over both film-maker and subject when it emerged that an early rough cut of the documentary featured footage of Doherty mutilating himself with a broken bottle - a sequence that the writer, director, producer and cameraman of the programme says was never meant for the finished version. "It was a one-off," he says, "and I didn't want to portray Pete as someone who wallows in a well of self-harm. That scene was never intended for broadcast. Without compromising what I do, I respect people's privacy."
It was a sentiment - perhaps an odd one in a maker of documentaries - that Pomphrey extended to Doherty's love life. His relationship with the model Kate Moss has, at least in part, fuelled the burning media interest, but Pomphrey plays down her contribution.
"Pete and Kate's relationship has happened since I started making the film," he said. "She does appear in the film, but it's not a big part of the story. For me to have concentrated on that would have been to belittle my motivation. His private life is his private life. Believe it or not, away from all the attention their relationship is actually very normal. They're very loving - but that's all I can really say about it."
Over the past few months, the newspapers have perpetuated the image of Doherty as a spaced-out wastrel - a stereotype exacerbated by his eccentric duet at Live8 with Elton John singing Marc Bolan's "Children of the Revolution", a performance that even Sir Elton afterwards admitted was "a mess".
But, Pomphrey insists, "the whole motivation of my film was to go way beyond the shallow tabloid interpretation and find out exactly what makes Pete tick". You'd never know it, he says, but "Pete is actually an extremely articulate and intelligent man. He's also very witty. He's great at accents and is a really good mimic."
Having made films about creative types such as Damien Hirst, Jimi Hendrix, U2, the Eurythmics, REM, UB40 and Keith Richards, Pomphrey was ideally placed to take on the project.
In the film, Doherty talks about "that rush, that absolute contamination of the soul with melody and music". Before becoming a film-maker, Pomphrey played guitar on the Eurythmics' first album and has performed live with the likes of Mick Jagger, The Edge, Dave Stewart, Chrissie Hynde and Suggs. So it was not surprising when Doherty's management approached him last summer.
"Pete was already becoming a phenomenon when I went to meet him before a gig at Bristol University last September," Pomphrey says. "A close of friend of his had told me beforehand that everyone who meets Pete instantly falls in love with him. I like to make up my own mind, but I must admit I was very enamoured of him." The admiration seemed to be mutual, according to Pomphrey. "Part of that is down to the fact that I used to be a professional musician, so I spoke his language. It was all, 'I taught John Lennon how to tie his shoelaces.'"
Pomphrey believes the tabloids continue to be drawn to Doherty because we are riveted by someone who seems to teeter on the brink of self-destruction. "We all love a car crash," he reflects. "If you travel down the M4 on a Friday night, the traffic always slows down as it goes past a wreck. Everyone does it, whether they're a politician or someone from a council estate. There's that morbid fascination within the human condition because it makes us feel better about who we are. People enjoy watching others mess up because it makes their own mistakes seem less pertinent."
It certainly seems that we can't get enough of this flawed, charismatic singer. To underline his popularity, there has already been one documentary about him this summer - Stalking Pete Doherty directed by Max Carlish, on Channel 4 - which Pomphrey dismisses as "a pile of dog cack".
It's true that people are mesmerised by Doherty's headlong, devil-may-care approach, but Pomphrey thinks it is often misunderstood. "Without being phoney, Pete really is a libertine," he said. "I don't mean in the amoral aspects of that word, but he has a very natural ability to live absolutely for the moment. He doesn't live for yesterday or tomorrow. That can be interpreted as irresponsible or rude or unreliable, but it's actually none of those things. He lives by his own belief system in a very courageous way."
The red-tops, however, don't see things in such nuanced terms. Pomphrey says: "The papers are attracted to Pete's rebellious indulgences because they revel in being censorious. From their point of view, Pete spends his time sticking two fingers up at society and breaking the law. To them, it's a life of total irresponsibility."
But, he adds with some vehemence, "they're missing the point entirely. Pete is in fact a very, very talented singer-songwriter. He writes in the most eloquent, poetic manner. He's very much from a different era. He's a true romantic, and that is why he's so loved by his fans. He's their Dylan."
Is it possible that the bad-boy persona is put on to generate column inches and album sales? Not according to Pomphrey. "There's a liberal smattering of Johnny Rotten/Kurt Cobain in there," he says. "Pete is a hybrid of many previous rock'n'roll personalities, but he's absolutely genuine. Some more cynical members of the rock fraternity have suggested that all he's done is read the rock'n'roll manual, but that's just not true. You can read all the manuals you want, but that doesn't give you talent. Pete's talent speaks for itself, and that's what gives him legitimacy."
But didn't he risk aggrandising the unsavoury habits? "There is a danger in any film-making of glorifying the subject, but I've tried to present a balanced view, so the audience will see how Pete chooses to lead his life, but also the dangers of leading such a life. Anyone foolish enough to try to emulate it would find out very quickly that it's not all a bed of roses. Pete talks openly about addiction. There is nothing romantic about addiction. If you listen to his lyrics, he doesn't talk about drugs. He talks about being a libertine in Arcadia, where one is able truly to be oneself."
Pomphrey has had privileged access to pop's most in-demand figure, but he was careful to maintain some detachment, not to get sucked into the Doherty entourage. "At times, I have felt like just another hanger-on," he says. "But I've done my best to go home at the end of the day and not become another member of the gang."
'Who the F*** Is Pete Doherty?' is on BBC3 at 10pm on SundayReuse content