On the surface, it has all the hallmarks of the cliched "difficult second album" syndrome. The ominous title. The fact that it has taken five years to follow up a resoundingly successful debut. The split from her songwriting partner, Ben Langmaid. But don't be deceived: Trouble in Paradise is one of the finest pop albums you're likely to hear in 2014.

After just a few minutes of conversation, it is apparent that its creator – or at least co-creator – Elly Jackson is not the kind of person to simply roll over and fade into professional obscurity. Speaking from her London home, the 26-year-old is shrugging off a bad head cold but is still capable of thoughtful, thought-provoking ruminations on how, why and when, all delivered in a likeably no-nonsense, matter-of-fact manner.

It's no surprise that Jackson is the articulate type: when her eponymous debut landed in 2009, both her music and her outspokenness on the "Ikea mentality" of youth culture marked her out from her peers. Here, at last, was a modern pop star with something to say and an intriguingly androgynous image. The album La Roux did the business on both sides of the Atlantic, even bagging a Grammy in 2011. A heavy period of touring followed. Then silence.

“There are so many factors that made this record take the time it took,” she says. “The recording took about two years. For me, that doesn’t seem that long, but for a lot of people that is a ridiculous amount of time. Most people would never be given that much time with a producer, because it would cost way too much money and because the producer would never give up two years of their life to one band or one artist. So me and Ian [Sherwin, who had previously acted as engineer] just worked together.”

Working with a multitude of producers, as so many pop artists do these days, was never an option. “The reason that I don’t work with many producers is because (a) I don’t have a personal connection with them; and (b) [with them] I only have a limited amount of time, which I’m not really interested in. Actually, we were given a time limit, but we just ignored it and said, ‘Leave us alone, we’ll let you know when it’s finished’,” she says with a chuckle. “So that’s part of it – but then also there’s the fact that I wanted to do something a lot braver, production-wise. Just generally, I wanted to do something braver. I wanted to become – I needed to become – a better musician to pull that vision off. So that did take a while. There are elements of perfectionism in there and elements of dysfunction, too.”

The process of creating album number two wasn’t as straightforward as navigating dysfunction and vague deadlines, however. The success of the debut brought many high points, but it also led Jackson to a place of crippling anxiety that affected her ability to sing. At one point, she thought she might have had throat cancer, but treatment for performance anxiety eventually curbed the problem.

"It affected everything in a weird way," she says. "It affected my mood in the studio for a long time, it affected my vocals, it affected the keys of songs and all sorts. But in terms of literal content, Silent Partner is directly about that situation."

The split with Langmaid

That brings us to the split with Langmaid. Previously, the pair had enjoyed a similar set-up to Goldfrapp: Jackson was the face of the band and toured and gigged their songs, while Langmaid remained the studio-based partner, although they both co-wrote and co-produced.

Jackson is reluctant to go into details about exactly what happened – and Trouble in Paradise contains six songs co-written with Langmaid – but, while Silent Partner may relate to her voice issues, it simultaneously seems like a not-so-veiled jibe at her former bandmate. "You're not my partner and you're not a part of me," is one line.

“Our creative partnership had run its course, but there were other reasons behind it,” she says. “They’re quite personal and I think it would do a disservice to both of us for me to discuss them. But there were quite fundamental differences between us, and that was it, really.”

She opens up a little more when I ask whether the possibility of not making a second album at all and simply leaving a cracking debut behind appealed to her at any point over the last few years.

“Oh my God, that’s like my worst nightmare,” she cackles, choking back a coughing fit. “No, I can’t imagine anything worse. That would be my idea of hell, basically, and I think that’s the fire that kept me going: the thought of just leaving behind a debut.

“I mean, let’s be honest: I knew that I was a one-hit wonder, it’s not a secret. I saw the problems in the first album and I guess Ben didn’t. I saw it as extremely trapping, musically, extremely trapped in a zeitgeist that was no longer. And also, how I had presented myself as an artist didn’t have any longevity whatsoever, and I was upset at myself for starting my career in that way, because it’s not the career that I wanted. I never, ever cared about having a number one hit single or anything like that; it’s never the artist I wanted to be. So for me, my biggest ambition was to start again as the artist I should have started as in the first place.”

Potential collaborations 

Rumours of her collaborations with Nile Rodgers and London indie band White Lies were only half

true; she has written a couple of songs “of a very high standard” with Charles Cave and Harry McVeigh from White Lies, “but they weren’t right for this record, and they maybe weren’t La Roux tracks”, she says.

“They might be things that I look at again in the future, but they’re maybe more appropriate for a side project of some kind. No, I didn’t end up working with Nile Rodgers. We hung out once or twice, and again, enjoyed each other’s company greatly, but we never actually worked together musically.”

It's not as if she needs a leg-up or any sort of helping hand, anyway: the new, more confident, practical Jackson is more sure of her vision for La Roux than ever before. Her self-assurance is audible in the zing of songs such as Kiss and Not Tell, Uptight Downtown and Sexotheque, all earworms that nail that magic formula of memorable melodies and lyrical depth. This album, she says, is a much truer representation of her personality than the debut was.

“I think I almost became a different person for a few years, and it wasn’t true to who I am, and who I’ve been for my whole life,” she says. “I was definitely slightly disappointed that I fit in as much as I did, because when we started making that [debut] album, the sound certainly wasn’t the kind of thing that was on the radio – and by the time we released it, it had become more of a zeitgeist, more of a ‘thing’. It put me in an area that I didn’t really want to be in: that chart-topping pop area. I don’t mind if you top the charts by being different, but I guess that most people did see that as being different.

“That started to eat away at me a little bit. I’m not going to say that I didn’t enjoy it at the time, because I did, but I think I was living in a slightly different personality, which is probably why I came up against psychological problems with my voice and stuff later.”

Does that mean she is happy with the “perennial outsider” label these days?

“Well, I don’t feel like I fit in at all, which is more true to how I’ve felt throughout my life. I guess that’s why I feel more comfortable with that label now.

“That could be my downfall, I don’t know, but it certainly feels more true to me that I’m an outsider. It feels a little bit more like a minor rebellion against a lot of very simplistic, quite crass dance music that’s out there at the moment. If that makes me an outsider, so be it.”

Trouble in Paradise is out now. La Roux play Dublin's Academy on November 12