La Roux received positive reviews from most music critics. At Metacritic, which assigns a normalised rating out of 100 to reviews from mainstream critics, the album received an average score of 76, based on 16 reviews, which indicates "generally favorable reviews".The Guardian's Alexis Petridis wrote that "[t]he sound is authentically tinny, bass being something that most synthpop pioneers seemed to think the gleaming 'Music Of The Future' could do without. The rhythms tend to a clipped, funkless boom-crash that listeners of a certain vintage may find difficult to hear without picturing a school disco dancefloor packed with fourth-formers trying to 'do' robotics." Steve Harris of Clash referred to the album as "[t]he ultimate expression of '80s love" and stated that "apart from a couple of later tracks, the album is far from filler and still delivers blow after blow of superb songcraft." Luke Turner of the NME raved that "with this astounding debut, an unassuming 21-year-old from SW2 has revitalised a forgotten form to make one of the finest forward-thinking British pop albums of recent memory." Heather Phares wrote for Allmusic that "La Roux's dedication to their aesthetic makes this an album where the songs are variations on a theme, and on the rare occasion where the songwriting isn't razor-sharp, the style threatens to overtake the substance. However, that devotion also makes La Roux a standout, not just among the many other '80s revivalists, but the entire late-2000s pop landscape."
Slant Magazine reviewer Paul Schrodt described La Roux's sound as "frosty, uniquely British, deliberately affected, and anything but casual", but added that "it's the band's attempts at vulnerability ('Cover My Eyes') that make for the most insipid listens."Pitchfork Media's Joshua Love noted that "La Roux delivers icy but irresistible throwback pop that hearkens back explicitly to fellow femme-led Brits Yazoo and the Eurythmics." Talia Kraines from BBC Music wrote, "That shrill vocal might mean the self titled debut album is not something you're likely to listen to all in one go in a high pressure situation, but it's one jam-packed with killer pop song after killer pop song."Peter Paphides of The Times remarked that "[f]or the almost militant purity of its execution though, La Roux inspires a peculiar sort of awe. Exclusively using keyboards is one thing, but the Brixton-based duo have gone a step further, purging their sound of any keyboard noise that bears even a passing resemblance to what your Jeremy Clarkson sort of music fan would refer to as a 'real' instrument."Rolling Stone's Rob Sheffield commented that "[a]long with co-writer and fellow synth dude Ben Langmaid, she's ruling U.K. radio with splashy dance hits about sex and betrayal", naming "Bulletproof" the album's "definitive gem".Simon Price was critical of the album in his review for The Independent, stating that "[m]uch of the time, La Roux sound strangely distorted, like the backing music from an early 1990s Sega Mega Drive game turned up to 11."
"Quicksand" was released as the album's lead single on 15 December 2008. The song charted on the UK Singles Chart at number 153 and was accompanied by a music video directed by Kinga Burza. It was re-released on 23 November 2009, re-entering the chart at number 129. "In for the Kill", released as the album's second single on 16 March 2009, peaked at number two on the UK Singles Chart for four weeks and its music video was directed by Kinga Burza. The single is so far the duo's biggest hit (although it peaked one place lower than follow-up "Bulletproof"). It became the UK's fifth biggest seller of 2009 and thirty-fifth biggest seller of the 2000s decade. This was despite the song debuting at number eleven, taking three weeks to reach the top ten and five weeks to reach its peak of number two. The song is also known by a dubstep remix from Skream, called Skream's Let's Get Ravey Mix. "Bulletproof" was released as the album's third single on 22 June 2009, becoming La Roux's first chart-topper on the UK Singles Chart, and was accompanied by a music video directed by The Holograms@UFO. "Bulletproof" sold 80,144 copies in its first week in the UK, although it failed to outsell "In for the Kill" overall. The single also charted at number five in Ireland, thus topping "In for the Kill" in both countries. It was featured as the Single of the Week on the US iTunes Store from 22–29 September 2009.
"I'm Not Your Toy" was released as the album's fourth single on 28 September 2009. Jackson explained to The Guardian on 22 July 2009 the reason why the song came out during the summer: "I think sunny weather drives you towards certain tempos and melodies that work well booming out of open windows." She added that the duo demanded that the single was released in summer "for that reason. It has a brightness that wouldn't work in winter." It peaked at number twenty-seven on the UK Singles Chart. On 15 July 2010, Jackson uploaded a behind-the-scenes preview of the music video for "Tigerlily" on YouTube talking about its theme. However, neither the single nor the video have surfaced as yet.
Most of the sounds from the album were individually sampled for live performance - triggered by midi controllers and sequencers - or emulated using computer based soft-synths and plugins. Additionally, two Nord Lead 2x virtual-analog keyboards were used as a substitute for certain sounds, played by fellow band members Mickey O'Brien and Mikey Norris. A Minimoog made an appearance during a 2009 performance of Bulletproof on British TV Show, GMTV, but was rarely used again. It was subsequently replaced with a Moog Little Phatty keyboard.
Frequent application of various distortion, overdrive and bitcrusher methods give the album its signature sound. In an interview with Musictech.net, Ian Sherwin (credited for mixing the La Roux album) said there was a lot of "...slamming audio through analogue circuits for natural overdrive. The input circuits of a Minimoog, a VCS3 and an old clapped-out Revox tape machine were all regularly abused. I also used the SSL desk at Rak Studios in a way that I hadn’t before – outside of a mix at least. I had a multitude of effects, distortion and parallel compression running off the groups so that I could quickly put together a sound from what I was given and then fly that back to Ben’s computer. That was a lot of fun and really intuitive because I had so many colours available at my fingertips."