Andrew was born on the 25 November 1971 in Anglesey. He grew up on the Isle of Anglesey in Wales, and was state educated at Ysgol David Hughes in Menai Bridge. After leaving school he worked for the then Department of Social Security. In 1994 he took a job with the British Heart Foundation, before roles at Hope House Children's Hospice and East Lancashire Hospice. Before being elected to parliament he led the fundraising team for Martin House Hospice.
Andrew was first elected as a Conservative councillor in Wrexham in 1995. He then stood unsuccessfully as the Conservative candidate in the 1997 Parliamentary election in Wrexham. In 1998, whilst still serving as a councillor he defected to the Labour Party, citing issues with the "direction of the party".
Two years after losing his council seat, he rejoined the Conservative Party and moved to Leeds. He served as a Leeds City Council Councillor from 2003 to 2010, initially representing the Aireborough ward, and following boundary changes representing the Guiseley & Rawdon ward. He was elected as Member of Parliament for Pudsey in the 2010 general election, taking the seat from Labour.
On 22 February 2012 Andrew was headbutted and punched in a House of Commons bar during a disturbance created by Scottish Labour MP Eric Joyce, but tweeted the next day that, "I'm OK." Joyce was charged with common assault, A fourth charge was added on 9 March. fined £3,000 and ordered to pay £1,400 in compensation to Andrew and other victims, but not given a custodial sentence. In a statement before the House of Commons on 12 March 2012, he apologised personally to his victims, stated that he had resigned from the Labour Party, and that he intended to complete his current term as an MP but not seek re-election.
In 2012, Andrew brought forward a bill that would create a new power for Governors to "Destroy or otherwise dispose of any unauthorised property found within a prison or an escort vehicle". The bill was supported both by the Coalition and also the Labour Party with Shadow Secretary of State for Justice Sadiq Khan saying he backed the bill.
During the debates on the Marriage (Same Sex Couples) Act 2013, which he subsequently voted for, Andrew responded to comments from Gerald Howarth about "aggressive homosexuals" by telling of a time when he had been attacked in the street and beaten unconscious "because of who and what I am".
At the 2015 general election, the Pudsey seat was considered to be one of the most marginal in the country. However, Andrew retained the seat through increasing his majority to 4501.
In January 2016, Andrew was one of 72 MPs who voted down an amendment in Parliament on rental homes being "fit for human habitation" who were themselves landlords who derived an income from a property.
In May 2016, it emerged that Andrew was one of a number of Conservative MPs being investigated by police in the United Kingdom general election, 2015 party spending investigation, for allegedly spending more than the legal limit on constituency election campaign expenses. However, in May 2017, the Crown Prosecution Service said that while there was evidence of inaccurate spending returns, it did not "meet the test" for further action.
Andrew was appointed Vice-Chairman of the Conservative Party, with particular responsibility for cities, on 23 September 2016.
In Parliament, Andrew served on the Welsh Affairs Committee between November 2010 and November 2012, before becoming Assistant Whip (HM Treasury) in June 2017 and Parliamentary Under-Secretary (Wales Office) in January 2018. He currently serves as the Parliamentary Under-Secretary (Ministry of Defence).