Crosby first ventured into overseas politics at the 2005 United Kingdom general election, where he managed the Conservative Party's unsuccessful campaign. He has since also run Conservative campaigns for the 2008 and 2012 London mayoral elections, as well as the 2015 general election, all of which resulted in victories for the party. His campaign was not successful for the 2016 London mayoral election (which was won by the Labour candidate, Sadiq Khan) and the 2017 general election in which the Conservatives remained the largest party but lost 13 seats and their parliamentary majority.