Active in politics since the 1970s, he was a Young Conservative branch founder whilst still at school, and in 1976 proposed the legalisation of cannabis at a Young Conservative national conference. His mother Elsie was already a councillor when he was elected a councillor in Hillingdon in 1982, and he was Leader of the Council between 1990 and 1992. In 1992, he stepped down to run for Parliament, defending the marginal Hornsey and Wood Green constituency, but he lost the seat to Labour's Barbara Roche. Boff ran in the safeLabour seat of London South Inner in the 1994 elections to the European Parliament, and was placed seventh on the Conservative list in London in the 1999 election. He failed to be elected both times.
He contested the Conservative nomination for the London mayoral elections in 2000, 2004, and 2008. He came second in 2000, behind Steven Norris, and came second once again in 2008. He was placed first on the Conservative top-up list for the London Assembly in 2008, comfortably winning a seat. He was re-elected in 2012 and 2016. He ran for chairman of the Assembly in 2010, with the backing of the 11 Conservative members, but lost to Liberal DemocratDee Doocey, who received the backing of the 14 other members, including Richard Barnbrook. After his re-election to the Assembly Andrew was elected as the GLA Conservative Group Leader. In September 2015, Boff called for a managed street prostitution zone to be set up in East London in order to protect sex workers from harm. In summer 2018, Andrew launched his campaign to be the Conservative candidate for Mayor of London. He was shortlisted along with Joy Morrissey and fellow London Assembly MemberShaun Bailey. Boff finished in second place with 35%, an increase of 31% on his run for the nomination in 2015. In 2019, Boff became Chairman of the Confirmation Hearings Committee and the Planning Committee.
He has run for office numerous times in Hackney, where he lived. He received the Conservative nomination for the elections in 2002 and 2006 to elect the Mayor of Hackney, but came second both times. He was the Conservatives' London Assembly candidate for the North East constituency in 2004, but came third, behind the candidates from both Labour and the Liberal Democrats. He achieved success in Hackney in 2005, when he won the supposedly safe Labour seat of Queensbridge in a council by-election, before losing it at the 2006 Hackney Council election, albeit with a vote tripled from the previous borough election. Boff ran for Mayor of Hackney for a third time in 2010. A booklet containing election statements from every candidate was distributed to every voter in the borough, but excluded Boff, due to the council's confusion over whether the statements he made about the cost of the mayoralty were legally admissible. By the time they decided that they were, it was too late to print, and the council compounded this by telling voters who enquired that Boff was not running. In the contest, Boff fell to third place, behind the Labour incumbent and the Liberal Democrats.
