Paloma Faith is an unusual pop star. Her flamboyant, retro appearance is upholstered by a deep-thinking mind and she articulates herself in an uncut East London accent. She hangs out with the author Hanif Kureishi and you can expect to find her at an art opening. When we meet in London’s Soho House, she is a cocktail of reds and oranges. Her hair, held back by a neon scrunchie, is white gold after the ‘gingerness’ washed out in the sea and she’s wearing a red-and-white checked gingham skirt with Chelsea boots.

Although she admits that by keeping slim she makes a concession to conformity, she otherwise seems to do things her own way. She told the head of the record label who eventually signed her to stop texting during her showcase — unthinkable for an aspirant artist in the cold world of the music industry. ‘I said if he had anything to do with my career I’d rather sing in pubs for the rest of my life and walked out. Nine months on he wrote me a letter of apology and said he wanted to sign me.’

Faith had been pulling pints while studying for a Masters in directing and designing for the theatre at art college. She was scouted by the record label after the pub manager asked her to front his band. Today, she’s promoting her third album. The first two went double platinum and the second, Fall to Grace, reached number two in the UK charts.

The new album is called A Perfect Contradiction. The title comes from a conversation with the megastar producer Pharrell Williams. ‘I said, “I’m interested in perfect contradictions, somebody who thinks one thing but they are another, because I consider myself to be that.”’ There is, she says, a joyfulness, euphoria and hopefulness to the record. ‘Even though I still acknowledge that sad things have happened, it’s more like the Paloma that I present. It’s got a humour to it and it’s uplifting — even when its subject matter is sadder [than on my last album] — “If it’s all gone to shit, let’s dance.”’ You can’t, she says, experience joy without experiencing agony first.

Faith’s parents divorced when she was two and she was brought up by an English mother who preached rejuvenation. If she didn’t like something about herself, she was encouraged to act on it. ‘What she taught me — and this works — is that if you decide to change something, at the beginning you have to force it, but eventually it just becomes instinctive. If you’ve done it enough times it becomes you.’ She would, she says, be wasting her life if she wasn’t constantly evolving.

Faith did know her Spanish father growing up but hasn’t spoken to him now for six years. She doesn’t go into details, but separation, loss and abandonment animate her. They’re a theme of the album. ‘I just feel that all my work’s about that. That’s my niggly thing — separation and the idea of [the] impermanence of those things. I’ve only felt unconditional love from my mother in my life ever and I feel full of fear because of it.’

At the start of her single ‘Can’t Rely On You’, she says in Italian, ‘Love is loss. Loss is love.’ The characters in the music video, she says, are all involved in different male–female relationships, and have to deal with abandonment and loss, or her leaving.

There’s the surgeon who is the ‘hyper-real accentuated version of the therapist, where you become completely dependent on that person but when the work is done [the relationship] ends’. A type of ‘abandonment’, according to Faith. And the chauffeur who drives her everywhere but who leaves because she drives him mad with constant nagging. ‘The lover character is the only one I leave and I leave out of fear.’ Because she doesn’t want him to leave her? ‘Yes.’ Is that because her father left? ‘I would imagine. I don’t know. I’ll let you figure it out.’

Faith tries to fill the void created by estrangement from her father through bonding with older men. Hanif Kureishi is one. ‘I think I have that quite a lot. I had it with Terry Gilliam and with Timothy Spall when I met him. These men that I really admire and really value I go to with an agenda. I know they can teach me something that I wasn’t taught because I didn’t have that guidance from a male perspective.’ She was cast by Gilliam in his Imaginarium of Doctor Parnassus and she appeared in the BBC comedy Blandings with Spall.

Faith has said before that she was a shy girl and that acting in the school play helped her emerge from her introversion. The shyness, she realised, belonged to her and not to her character on stage. The flamboyance of her appearance is, in a way, she says now, her war paint. ‘I definitely think it’s protective.’

Faith has forced herself to become confident. But, occasionally, her former self creeps back. ‘The last two weeks I’ve had quite a lot of depression and I didn’t realise why — it took me a while to process it, but I feel really vulnerable and I feel like that introverted version of myself was rearing its head. I was becoming a bit agoraphobic and not answering the phone… And so I see it’s still there but it’s buried. I have to get dressed up and go out and do this — it becomes me then.

‘I’m quite good sometimes at acting — I see myself on television when I’ve been feeling absolutely awful and you couldn’t tell a sod that I was in a really awful place. My mother always knows but most people won’t recognise it.’ Some ‘pretty dark stuff’ has happened in her life. What, she doesn’t divulge. Her therapist tells her to be kind to herself, to the child in her, and to ‘talk to little Paloma. I always laugh when he says that.’

She’s ‘a bit scared’ of the months of promotion that stretch out before her. Working life is bookended by what she loves — writing and touring. Selling herself is the scary bit in between. And winning over the airwaves has been hard. Although Radio 2 is ‘amazing’ to her, ‘all the others obviously don’t like me’, she says candidly. ‘They’ve decided I’m not for them, even though I’m writing my first single with the biggest producer in the world [Pharrell].’

Faith doesn’t want to be pigeonholed. ‘Journalists say, “You contradicted yourself a while ago,” and I say, “Do you think you’re clever for noticing that? Do you feel proud? Because actually I think both.”’ She insists on the right to think one thing one day and another the next. ‘Knowing yourself is knowing that you’re changeable on an hourly, minutely, basis…You can’t summarise anyone in a headline, can you?’

Faith finds it hard enough to summarise herself. ‘I’m bipolar,’  she says, laughing again. ‘No. I don’t think technically I am. But I’m quite erratic. But no, I wouldn’t say that, I’d say I’m sensitive. So I’m affected.’