Madley began his refereeing career on the local Wakefield leagues. He quickly advanced through the levels before becoming a Level 3A referee in 2008. This allowed him to act as an assistant referee on the three Football League divisions. The following year he was promoted to the Panel List which allowed him to referee in the Conference divisions. He then progressed further the following year by becoming a Select Group Assistant Referee, officiating on the Premier League. In 2011, he progressed to his current role, a National List Referee, officiating in the three Football League divisions. Andrew is the older brother of former Select Group Referee Robert Madley.
For the start of the 2016–17 season, Andrew was included as a Select Group 2 referee which sees him primarily referee in the Championship. He took charge of a Premier League game for the first time on 31 March 2018, a 2–2 draw between Watford and Bournemouth.
In June 2019, Madley was promoted to the Select Group 1 Referees list which will see him referee primarily in the Premier League.[2]