Might the 2 million people worldwide who bought the throwback synth-pop of La Roux’s debut still be listening? (Can one even have nostalgia for a revival?) Absent for five years, Elly Jackson is banking on the likelihood that her Grammy-approved, rinky-dink missives have indeed been missed.

Her second album arrives after two frustrating false starts — a hush-hush UK tour in early 2013 and an appearance at the US Coachella festival shortly afterwards. The internet ripples that greeted both suggested that the world was still holding out for the cooing androgyne whose flaming quiff has now turned into a more glamorous directional swish, no less 80s for its coiffedness.

We now know why Trouble in Paradise took so long. Along the way, Jackson lost her trademark falsetto to performance anxiety. And then she lost her right-hand man, Ben Langmaid — long assumed by sexists to be the silent partner actually doing all the work — to musical differences; Trouble in Paradise is aptly named. You get the fame, the unpronounceable cocktails on tap, an entre into the luxe life — La Roux twice collaborated with Kanye West — and all sorts of unforeseen bother besides.

On Trouble, the percolating Silent Partner (strong whiff of Depeche Mode, faintly Billie Jean bassline, Batman-theme outro) would appear to be about Langmaid; the split was acrimonious. “You’re not my partner/No you’re not a part of me,” she declares.

But in some interviews, La Roux now seems to be suggesting the song is about her own troublesome silence, when muscular tension would not let her hit her high notes. A specialist has since helped Jackson find her way back up to her ceiling; producer Ian Sherwin now fulfils the role of sounding board.

The sex factor has increased severalfold since the last record — just check the song titles. But this is no hot and steamy affair. Getting it on still feels a curiously chaste pastime here, thanks to all those keyboard sounds from electronica’s infancy, and La Roux’s predominantly sweet girlish vocals. She is all for kissing, but not telling (“all I want is to come out of my shell,” yearns Kiss And Not Tell), a white funk galumph that confirms La Roux and Sherwin have been studying the excellent Tom Tom Club.

Cruel Sexuality has an innocent melody and a baffled chorus: “Oh, you make me happy in my everyday life/ Why must you keep me in a prison at night?” La Roux sings, indicating she probably didn’t read much 50 Shades of Grey as light relief from battling her larynx and Langmaid. There’s not even all that much sonic smut to an excellent tune called Sexotheque. Here, she examines the night-time habits of sleazebags with sweet-natured equanimity. It’s an absolute corker of a song, strung round a chirpy keyboard hook you could play with one finger; the chorus is both hilarious and rhythmically deft. “He never answers the phone/ Oh I’ll bet money money money/ I’ll bet/ He’s at the sexotheque,” it goes.

Exotic holidays and discotheques were, of course, favourite tropes of the original 80s set — Club Tropicana, for one — and here, La Roux sets out a humid scene full of “tropical chancers” lurking under “cigarette trees”. Paradise Is You — built for slow-dancing — turns its nose up at the palm trees. On this persuasive second outing, the endless beach seems a grey and loveless place without the object of La Roux’s desire.