[1] "New Year" was written by the group's members in collaboration with Cameron McVey, Jony Lipsey, Matt Rowe and Felix Howard.

[10][11][12] It contains acoustic instrumentation in the form of beats, bass, strings, guitar and keys,[3][9] and features tight production juxtaposed with the group's harmonious vocals.

[9] Writers for the BBC characterised the song as having "a melodic swagger" reminiscent of All Saints' earlier work, and a "classy arrangement [...] boosted by an infectiously splashy drumbeat and stabs of acoustic guitar".

A journalist from the BBC wrote that the single as "lives up to the hype" and praised the inclusion of lyrics about Christmas as "without sounding remotely contrived".

[11] The Sunday Herald's Samuel McGuire interpreted "New Year" as a "mellow [and] dewy-eyed" song that will "undoubtedly cement [the Sugababes'] 'new All Saints' tag early in 2001".

[17] Eva Simpson of the Daily Mirror gave a positive review, writing: "Taken from outstanding debut album One Touch, this soulful track is head and shoulders above other festive releases.

[21] In December 2012 Bernadette McNulty of The Daily Telegraph picked it out as one of the newspaper's favourite Christmas songs: A relentless tearjerker from the pouty North London teenagers off their debut album.

Sneakily giving the song a title that makes it last throughout the festive season, this updates old school girl-group harmonies from Christmas classics by the likes of the Ronettes with a clunky drum beat.

[29] The Daily Telegraph's Bernadette McNulty described their appearance in the clips, writing: "The original trio sulk their way through the video in boot-cut jeans and smudged eyeliner".

[32] The song was covered by Welsh indie pop band The Darling Buds and released as a digital single on Oddbox Records on 15 December 2018.