Burton was born in Northampton, England, but was brought to New Zealand by his family when ten years old. He attended high school in Wanganui. He has been involved in a wide range of social and community organisations, including the Red Cross, the Department of Social Welfare, the Central Plateau Rural Education Activities Programme, the Council of Social Services, the Taupo Employment Support Trust, and the Taupo Sexual Abuse Counselling Service. He received the New Zealand 1990 Commemoration Medal for his work.
In the 1993 elections, Burton stood as the Labour Party's candidate for Tongariro, an electorate in the central North Island, defeating Ian Peters. This later became the seat of Taupo, which Burton retained.
From 1996 to 1999, he served as his party's Senior Whip.
When the Labour Party won power in the 1999 election, Burton became part of the new Cabinet, assuming the roles of Minister of Internal Affairs, Minister of Defence, Minister for State-Owned Enterprises, Minister of Tourism, and Minister of Veterans' Affairs. In 2002, Internal Affairs and Veterans' Affairs were transferred to George Hawkins. In February 2005 he became the Minister of Treaty of Waitangi Negotiations, and dropped the State-Owned Enterprises portfolio.
In late 2004, with Jonathan Hunt set to retire from politics, Burton was regarded by many as the Labour Party's preferred choice to replace him as Speaker of the House of Representatives. In the end, however, Labour decided to nominate Margaret Wilson for the position.
In November 2007 Burton resigned from his Cabinet positions during Prime Minister Helen Clark's portfolio renewal. When Labour's party list was written prior to the 2008 general election, he was given a low placing of 39. He then lost his seat in a nationwide swing to the National Party, and due to his place on the list, was not returned to parliament.
Burton stood unsuccessfully for Taupo District Mayor in the 2010 local body elections. After Darren Hughes resigned his list seat in 2011, and the next person on the Labour Party list, Judith Tizard, declined to take it up, Burton was entitled to reenter Parliament for the remainder of the term. However, he also declined the offer.
