Heather Peace is talking gay role models, love triangles and second chances.

This time two years ago, she confesses, it would have been hard to imagine her speaking about any of the above. In acting terms she was mostly resting and her music career was no more than a hobby. It was a period Peace describes as her "dark years".

Then in October 2010 that all changed. Her role as "hot cop" DS Sam Murray in BBC Three drama Lip Service has seen Peace afforded cult status, with a legion of besotted fans. There are online forums dedicated to dissecting her every on-screen move, while she has gone from playing gigs to a handful of people to selling out major venues.

Set and filmed in Glasgow, Lip Service charts the lives and loves of twenty- and thirty-something lesbians. Central to the plot is a love triangle involving Peace's character and Cat, played by Laura Fraser, who is torn between her new girlfriend and first love Frankie (Ruta Gedmintas). It has divided Lip Service's devotees firmly into two camps: Team Sam or Team Frankie.

In a Glasgow hotel, Peace's expression is somewhere between baffled and bashful. "I knew there was a market for the show because there just isn't enough representation of the gay community on TV unless it's stereotyped," says Peace, who has been with her partner Ellie for two years. "It's the first time we've seen a drama [about gay women] that is about human emotions and not issues.

"As much as I loved [American TV drama] The L Word, it was like: 'Where are all the straight girlfriends and boyfriends we have?' I'm not just surrounded by gay women, I have friends from all walks of life." The affection for her character has perhaps been the biggest surprise.

"I saw it as a very minor role so that was a shock," she says. "The reaction from the [gay] community has been positive and I have lots of straight friends who love the show too.

"There are always going to be people who say: 'That doesn't represent my life.' You are never going to please everyone. For me, what is important is that it's a universal love story. I think Lip Service stops being simply a gay show because of that."

The second series of Lip Service, written by Harriet Braun, will air this month – which is just as well given its fans are getting mightily impatient. "I don't know why it takes them so blooming long," says Peace of the BBC Three schedulers. "I wish they would keep it in the same slot each year. The fact is, if we do a third series, all of us women are going to be four or five years older than when we started and have all of these nudity scenes. It's like: 'I'm now five years older – can we move it along a bit?'"

She makes a good point. Not that the fans would be complaining. Google "Heather Peace" and you get the feeling she could blow her nose and their affection for her would be no less ardent. Still, while we're on the topic of nudity, Lip Service certainly doesn't come up short on that front.

Peace, 35, vowed when she was younger she wouldn't strip on screen. Has doing the show seen that mindset change? "You have to find a reason for being naked." So it can't be gratuitous? "Oh, it can be gratuitous. Certainly, Ruta [Gedmintas] had to do that stuff – it was gratuitous for a reason because her character Frankie was so screwed up.

"I was proud to do the scenes in Lip Service because mine and Laura's were about making love and I think it dispelled a lot of those images of lesbians that you get in pornography. It was a true love scene."

Fraser isn't a fan of on-screen nudity, but has said it's easier to act opposite another woman rather than a man because they can share concerns over body issues and shyness. Fraser has expressed her gratitude that Peace, for example, helped hide her Caesarean section scar.

"We were able to cover each other as was required," confirms Peace. "Ruta had a different actress every day so it must have been difficult for her. Laura and I, though, once we got that initial sex scene out of the way, we had a real trust. We looked after each other."

With impeccable timing – just as we're getting to the juicy part – the hotel fire alarm goes off. Peace, though, appears impervious to the piercing din – testament perhaps to a previous role as a firefighter in ITV drama London's Burning – and, ever the professional, continues unperturbed.

"Getting naked in front of each other for the first time was quite hilarious, but we are all used to that now," she says. "I had to do a scene where I stepped out of the shower in front of Ruta. We were about to go for the take and I had my dressing gown on. Ruta said: 'Do you just want to open your dressing gown and show it to me now, get it out of the way?' and I was like: 'Er, no, you weirdo. Let's just wait until the take.'" Peace belly laughs at the memory.

Her previous television roles have also included an SAS sergeant in Ultimate Force, a single mother in The Chase, written by Kay Mellor, and most recently a teacher on BBC One's Waterloo Road.

Yet as a gay woman with a pivotal role in a lesbian drama, Peace has found herself under most scrutiny. "I'm under no illusions that if Ruta Gedmintas was gay I don't think there would have been half the attention on me that there has been," she says, grinning, before pausing and looking thoughtful. "By doing the show people are talking about my sexuality."

Is that difficult? "I guess I'll have to see. It was only professionally that I didn't speak about it because people often think, because you are gay, you can't play certain roles or imagine you acting opposite a boy. In the past, though, most of the roles I've played have been straight.

"I'm not sure how publicly it is out there apart from in the gay scene," she adds. "When I did London's Burning I would walk into Asda and everyone would look at me. The difference with Lip Service is that I can go into Asda and no-one will pay me any attention, but if I go into a gay bar then lots of people recognise me. It would be nicer if I was more visible – but more visible in a straight world too."

One of the biggest adjustments, she says, has been getting used to the spotlight being on her life away from work too. "Straight after the first series of Lip Service aired it was nervewracking because I'm essentially a private person," she says. "Even when I did London's Burning and Ultimate Force I only ever did interviews about the show – I never talked about myself.

"It has been tricky knowing people want to find out more about me as opposed to the character I'm playing. It is a role I'm taking seriously because most actresses and female singers who are gay don't feel they can talk about it. You have all these gay male role models, but still not that many women.

"The sad fact of the matter is there is an element of misogyny which stops gay women coming out. When a straight actress plays a gay role that's OK because it still has a heterosexual fantasy element to it."

Peace was voted Gay Icon of 2011 by G3 Magazine, aimed at lesbian and bisexual women, and ranked number 10 in the Independent On Sunday's Pink List – jumping 30 places from 2010. While she describes her newfound role-model status as "completely accidental", she says she is slowly, but surely, growing into that skin.

"It does bring an added pressure," she confirms. "I'm better with it now. A year ago I was struggling a bit with it because I thought, 'I don't really get this.' I didn't know what it's all about. I have sort of taken it on my shoulders now and feel grateful I can do it.

"I do feel a sense of responsibility I perhaps didn't feel when I was 23 or 24 and dealing with my own issues. Even if it's just a young girl being able to say: 'Mum, she's gay and, look, she's all right.'"

The youngest of two children, Peace was born and brought up in Yorkshire, her mother Barbara a counsellor and father Brian an odd-job man. She professes to having been a tomboy growing up. "I was always outside climbing trees and riding my bike," she says. "My mum once made me a broderie anglaise dress. She says I used to scream the house down whenever she tried to make me wear it."

Her childhood heroes included Doris Day, Judy Garland and Michael Jackson. Who did she have posters of on her bedroom walls? "Gabriela Sabatini," she says, smiling. "I had a serious boyfriend from when I was 14 to 19 and he asked: 'Do you think you might be a lesbian?' I said: 'Why?' And he replied: 'Well, you have Gabriela Sabatini posters on your wall and you don't play tennis -' I didn't have a clue, though. I just thought she was brilliant."

Peace had her first girlfriend at 19, confessing her feelings came as a surprise. "I had absolutely no idea whatsoever," she says. What made her realise she was attracted to women? "Kissing my first girlfriend on Canal Street [in Manchester]. I now look back and remember obsessive friendships at school and how, when they got a boyfriend, I felt a bit jealous. I only started piecing everything together after the event."

She and Ellie, 30, share a home in Brighton. When the topic is broached Peace's usual breezy candour evaporates. "I can't talk about Ellie," she says. "She is adapting to the attention I get. With her I'm just Heather."

Peace is back on steadier ground talking animatedly about doting over her niece, Neena, who is one year old. Is Peace feeling broody herself? "Yes," she says, laughing. "I would love kids." Has she set herself a deadline to have children? She shakes her head. "You can't. I will be the best auntie in the world if I can't have children myself. I would like to run an orphanage and have hundreds of kids running around. I love them. My heart and my life are totally open for children."

For now the focus is firmly on work. Peace was signed briefly to record label BMG in 2000, but it proved short lived when she cottoned on they wanted her to be "the next Martine McCutcheon".

She smiles sagely at the memory. "I released a cover of the Bette Midler song, The Rose, on the back of London's Burning, which reached number 56 in the singles chart," she says. "What happened? Well, the record company didn't release enough copies. I was probably quite a hassle for them, what with my contracted acting work. Usually people are signed to a label and they have ownership of them, which they couldn't do with me.

"I went from the high of being signed by a record label quickly followed by the crash of being dropped. I had the highs and lows all within the space of two months."

After parting company with BMG, Peace, then 23, thought her chance had gone, but Lip Service has helped breathe fresh life into that dream.

In the past year Peace has gone from performing in her local pub to selling out venues across the UK. I tell her I'm picturing knickers being thrown on stage, Tom Jones-style.

She throws back her head and laughs. "I've had quite a lot of fan mail but no knickers – yet," she says. "At first the demographic at my gigs was 30-plus women – the same age bracket as I am. More recently, though, I'm finding loads of young girls coming along and quite a lot of men too. That's great because I don't want it to be about me being gay."

Peace has just finished recording her debut studio album, Fairytales, which will be released next month, working alongside Oscar-nominated producer Nigel Wright, best known for his work with Andrew Lloyd Webber on Joseph And The Amazing Technicolor Dreamcoat and Jesus Christ Superstar as well as the movie soundtracks for Evita, Cats and The Phantom Of The Opera.

He and Peace became good friends during her London's Burning/BMG days and kept in touch. "I've been lucky because Nigel was going to oversee the album but not be in the studio – then he got addicted to the whole thing," she says. "He can't keep himself away.

"It's become a big sound in the end. We brought in a huge string session and a gospel choir. We were going to have a raw sound, but the songs lend themselves to big numbers."

The original title of the album was Sabotage. When I ask why, Peace smiles softly. "Dark days," she says. "The title was me being honest about having a couple of dark years. A couple of years before Lip Service there wasn't much work around and I didn't know what to do because I had only ever sung and acted since I was 10 years old."

Such was her despair she considered avenues new. "Weirdly, I did get an application form for the fire brigade," admits Peace, chuckling. "I never went through with it. I'm quite handy so I did a lot of painting and decorating for friends. I'm not proud. I sent text messages out saying: 'I'm struggling, does anyone want any work done?' I have always managed to pay my mortgage, but it has been tough."

Fairytales is much more reflective of where her life is now. Peace admits to being rather glad her first foray into the music business didn't pan out. "It would have been shortlived and I think in this career it's about longevity rather than the quick buck," she says. "I'm sorry it has all happened as late as it has, but I don't know if I have ever been mature enough before. It has taken me this long to get to the stage where I feel ready."

But back to Lip Service. If Peace was watching as a viewer, who would she want to see get together?

"Cat and Sam, without a doubt," she says. "It isn't just a safety net – Cat does love Sam. It's so easy to hark back to an ex-love, but there is a reason they are an ex in the first place. Certainly if I've ever got back with anyone in my life it hasn't worked a second time." Go Team Sam.

Lip Service will be shown on BBC Three from April 20 at 9pm. Heather Peace's single, Better Than You, will be out on April 30, followed by the album, Fairytales, on May 21. Heather Peace will play St Andrew's In The Square, Glasgow on May 23. Visit www.heatherpeace.com.