Matthew launched the TaxPayers’ Alliance in 2004 as a non-partisan grassroots campaign for lower taxes and better public spending. Under his leadership, the TPA has grown to become "arguably the most influential pressure group in the country" according to the Guardian, with over 60,000 supporters, 15 full-time campaigners and a high media profile.

Matthew also founded Big Brother Watch in 2009 to campaign for civil and personal liberties. Under the management of Alex Deane and Dan Hamilton respectively, BBW has become a leading voice in this debate, winning praise for its research and campaigns from leading activists such as Henry Porter and longstanding groups such as NO2ID.

From September 2010 to May 2011, Matthew took a sabbatical from the TPA and BBW to lead the NO to AV campaign in the nationwide referendum on changing Britain's electoral system. The NO campaign won by a margin of over two to one, defeating electoral reform by 67.9% to 32.1%. Following the result, one commentator said: "The campaign provides a new model of how campaigns should be fought. Elliott ignored the talking heads and ran a campaign that chimed with voters, not the metropolitan elite."

Matthew has been described by the BBC as "one of the most effective lobbyists at Westminster" and by Tim Montgomerie of ConservativeHome as "probably the most effective political campaigner that Britain has produced in a generation". In 2010 he was ranked by Total Politics as one of the top 25 political influencers in the UK.

In 2006, the TPA won the ConservativeHome “One to Watch” award and in 2007 the Bumper Book of Government Waste was awarded the Sir Antony Fisher Memorial Award. In November 2007, Matthew was presented with the Conservative Way Forward ‘One of Us’ award by William Hague and in December the TPA won the Stockholm Network's prestigious Golden Umbrella award for Innovation. In 2008, the TPA was named 'Pressure Group of the Year' by the readers of Iain Dale's Diary and in 2010 the TPA was awarded the Templeton Freedom Award for pioneering work on public sector fiscal transparency.

Matthew was born and brought up in Leeds, England. He moved down to London in 1997 to study at the London School of Economics, where he graduated with a First class degree in Government. After graduation, he worked for a number of MPs and MEPs in the House of Commons and the European Parliament. He has written four books on public spending: The Bumper Book of Government Waste (Harriman House, 2006); The Bumper Book of Government Waste 2008 (Harriman House, 2007); The Great European Rip-Off (Random House, 2009) and Fleeced! (Constable, 2009). In June 2007 Matthew was elected a Fellow of the Royal Society of Arts and he is on the Advisory Committee of the New Culture Forum.