Burrows was born on June 30, 1979 in Winchester and has stated that the first albums he bought were Bad by Michael Jackson and a compilation album titled Ballads by The Beatles. The first instrument he played was the cornet and he later transitioned into drumming.

Burrows joined the band in May 2004. He was discovered in open audition to replace the original drummer for the band, who left in early 2004. Since he joined Razorlight, the group have released three albums, Up All Night which reached #3 in the UK Albums Chart; Razorlight which debuted at #1 in the UK chart and Slipway Fires which debuted at #4. His first performance with Razorlight was at London’s Bull and Gate on 25 May 2004.

Burrows resides in Hackney with his wife and his two daughters Chloe and Joni. He has maintained a good friendship with the lead vocalist of Editors, Tom Smith, who has collaborated with Burrows on Funny Looking Angels and within Burrows’ solo discography. The two met at Glastonbury Festival in 2005 through Burrows’ friendship with Smith’s girlfriend Edith Bowman.

Burrows first released a solo album, The Colour of My Dreams, on 26 May 2008. The album was released to raise awareness and funds for the “Jack’s Place” Appeal at Naomi House, a hospice for children in his home town of Winchester. The Colour of My Dreams was written and recorded at home by Andy during Razorlight downtime, after he stumbled across a book of poems by an old family friend and set about putting them to music. Using just ‘GarageBand’ he began work in his flat and sings and plays all the instruments on the record.

On 5 March 2009, Burrows left Razorlight with immediate effect, after playing for five years with the band. Burrows explained that there were “personal reasons” for the split.

After Burrows left Razorlight, he almost immediately joined We Are Scientists. His first album with the band Barbara was released in June 2010. The band’s fifth studio album and Burrows’ second with them, TV en Français was released in March 2014. Burrows left the band in 2014, but is still considered their honorary brother.

Eleven days after he left Razorlight, it was revealed that Burrows had signed to Universal Records, the same record label as his ex-band. Six months later Burrows’ new band I Am Arrows played their first show. Burrows revealed that he was working with Noah and the Whale producer Eliot James and the album Sun Comes Up Again was released in August 2010 and reached number 38 in the UK Album charts.

Editors frontman Tom Smith teamed up with Andy to form Smith & Burrows – they released their debut album Funny Looking Angels in November 2011, an album of winter songs featuring the single “When the Thames Froze”.

Burrows’s solo project saw the release of his album Company on 22 October 2012, which received critical acclaim. All singles from the album were A Listed at Radio 2.

Burrows played drums on the Arthur soundtrack produced by Mark Ronson One of the songs is currently the theme tune to the ITV chat show, The Jonathan Ross Show. His drumming also features on the Ilan Eshkeri soundtrack to Johnny English Reborn. “Nice Try” from his I Am Arrows album features in the film Friends with Benefits. In 2012, Burrows was approached by the production company Lupus Films to work on The Snowman and The Snowdog, the follow up to the 1982 classic animated film The Snowman. Collaborating with Eshkeri, Burrows co-wrote the soundtrack to the new film as well as writing and performing the official single from the film, “Light the Night”. The flying-home sequence also uses an orchestral version of Burrows’ track “Hometown” from his solo album Company. The score was nominated for a BAFTA craft award in April 2013. In early 2015, Burrows featured on a re-recording of Kate Miller-Heidke’s song “Share Your Air”, replacing the vocals of Passenger.

In November 2013, it was announced Burrows would join Ricky Gervais satire-based band Foregone Conclusion for a nominal period of time as musical director. Before the close of that year the Burrows played three shows as MD and drummer of the band. The soundtrack of the film, David Brent: Life On The Road was co-produced by Burrows and Gervais and released via Gervais’ own label Juxtaposition, distributed through Caroline International/Universal.

In 2018, he collaborated with the British author Matt Haig for the album “Reasons To Stay Alive”. The songs were composed by Burrows while Haig composed the lyrics for his songs. In August 2018, the title track of the album was released. The album was released by Fiction Records on 1 February 2019, featuring further singles, ‘Handle With Care’ and ‘Barcelona’.