Get up at 5.30, morning prayer at 5.50, Mass at 6. Then breakfast, and after that, helping around in the kitchen, and midday prayer. Oh my God, that was a long time ago. I can’t even remember what we were doing in the afternoon.” Amid the curvy orange and brown decor of the retro-themed Menza restaurant in Budapest, the frontman of the Unbending Trees, Kristof Hajos, is trying to recall an average day at the Franciscan friary where he spent his 18th year.

If Hajos is sketchy on some of the details, it’s hardly surprising. In the 14 years since he looked in vain to the Lord for salvation, he came to terms with his sexuality and muddled through the ensuing years dependent on antidepressants. Whatever life has taken from him, his sense of humour seems to have emerged relatively intact. He has now put together an album of achingly lovely chamber-pop confessionals, Chemically Happy (is the New Sad), on which Tracey Thorn and Ben Watt have collaborated.

He says, perhaps unnecessarily, that he never planned it this way. Throughout his “unhappy twenties”, Hajos always imagined that if he sang in a band, he would use his beloved Jarvis Cocker as a template. Indeed, Pulp’s music seems to act as a Greek chorus to several of the most dramatic episodes in his life. Thrown out of the friary for being “too immature”, he moved back into the family home and “had a nervous breakdown”. Hearing Cocker’s psycho-sexual revenge fantasy I-Spy, Hajos says, “I found myself hysterically identifying with it.”

As he sang along to the words upstairs in his room, one wonders what his parents thought was going on. For better or for worse, their son didn’t waste any time telling them. “I hadn’t confronted my own sexuality while I was in the friary . . . It was like, ‘I’m not gay. I’m just w***ing while thinking of men.’ Then, once I realised, I told my parents very quickly. Within a couple of weeks, my mother was fine, but it has taken my father ten years to sit at the same table with my boyfriend.”

The words may read dramatically, but – rather like the music his group make – there is a laconic warmth to the delivery that you suspect is there deliberately to offset that drama. It was almost by stealth that Hajos turned the Unbending Trees from an idea into a band. He set about creating a MySpace site for some songs he had written to melodies by the classical pianist Balázs Havasi (himself a noted recording artist in Hungary). Then he added a couple more tunes by the bassist Peter Hary.

Among these was an early version of The First Day, whose redemptive, twilight feel became something quite magnificent when rerecorded. Containing the line from which the album gets its title, this is the lyric, Hajos says, that he wrote to chronicle his first fragile steps away from antidepressants into a world “after panic attacks”.

So, for a time, the Unbending Trees were a band whose three members had never all been in the same room together. Not that this stopped Hajos alerting the world to their existence. He set about befriending some of his favourite musicians on MySpace, among them Ben Watt, of Everything But The Girl, who – in the process of launching his own Strange Feeling label – asked them to make a record.

Hajos is clearly taken aback by the speed at which events have begun to move. When the Unbending Trees came to London last year for their first British show, he was invited for dinner with his bosses – Watt and Tracey Thorn, his wife and collaborator. “I had to start drinking immediately I was so nervous. Which was good in a way, because if I hadn’t been drunk, I wouldn’t have asked her to sing on the album.” Which, in turn, may mean that his Satie-esque coming-out hymn Overture may never have, um, come out of the closet.

Like Hajos himelf, Budapest is much changed since the early 1990s. The singer tells a story about the excitement that took hold of his neighbourhood after the installation of the first Coca-Cola vending machine. Cross the bridge over the Danube (built by Hajos’s Scottish great-great-great-grandfather Adam Clark) and take the funicular railway up the hill to the castle which overlooks the twin cities of Buda and Pest, and none of those changes are visible to the human eye.

We’ve just enough time to visit Hajos’s favourite place – an ornate wood-panelled tea shop called Ruszwurm Cukrászda which dates back to the Austrian rule of Emperor Francis I. “This was where my parents used to take me when I had been good,” he says. After everything that has happened, I suggest that his parents must be proud of him. “My mother always stands next to my boyfriend at the shows,” he says. “And when we start playing, she cries.” In a good way? “Yes,” he smiles. “Definitely in a good way.”

The Unbending Trees, London Luminaire, Kilburn, NW6 (www.theluminaire.co.uk 020-7372 7123) Dec 4; Chemically Happy (is the New Sad) is out now on Strange Feeling (www.theunbendingtrees.com)

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