"Quicksand" was released as the album's lead single on 15 December 2008, originally reaching number 153 on the UK Singles Chart. The song was re-released on 23 November 2009 and rose to a new peak position of number 129 on the UK chart.
"In for the Kill" was released as the album's second single on 16 March 2009. The song peaked at number two on the UK Singles Chart for four consecutive weeks, while reaching the top fifteen in Ireland and Norway, the top forty in Australia and the top fifty in Belgium.
"Bulletproof" was released as the album's third single on 22 June 2009. The single debuted at number one on the UK Singles Chart, becoming La Roux's first chart-topper. The track reached number three in Austria, number five in Australia, Belgium and Ireland, number seven in New Zealand and number thirteen in Germany. "Bulletproof" also became the duo's first entry on the Billboard Hot 100 in the US, peaking at number eight.
"I'm Not Your Toy" was released as the album's fourth and final single on 28 September 2009. Speaking to The Guardian on 22 July 2009, Jackson explained that the duo chose to release the single in the summer because she "think[s] sunny weather drives you towards certain tempos and melodies that work well booming out of open windows", adding that the song "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 discussing its theme. However, neither the single nor the video ever materialised.
La Roux received positive reviews from most music critics. At Metacritic, which assigns a weighted mean 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."