Pennycook was raised in a single parent family in South London. He attended Beverley Boys Secondary School comprehensive in New Malden, before securing a place at the London School of Economics and Political Science to study History and International Relations. He secured a First Class Honours (July 2005) and was awarded the CS MacTaggart Scholarship Prize for best overall degree performance in any subject. He subsequently won a scholarship to attend Balliol College, University of Oxford to read for an MPhil in International Relations. He joined the Labour Party at the age of 19.
While still studying, he volunteered with the Child Poverty Action Group working with the then Chief Executive, Kate Green. Before becoming an MP, Pennycook worked for a number of charitable and voluntary organisations including at the Fair Pay Network and the Resolution Foundation where he led on issues relating to welfare reform, low pay and working poverty.
Pennycook was a Labour Councillor for Greenwich West from 2010–2015, resigning in March 2015 just before the General Election. He also served as a trustee of Greenwich Housing Rights and was a school governor at James Wolfe Primary School in West Greenwich.
He has written multiple articles for The Guardian about the need for a living wage in Britain and has served on the Living Wage Foundation's advisory board.
In November 2013, he was selected as the Labour Party's candidate for Greenwich and Woolwich, replacing Nick Raynsford who was retiring.
In May 2015, he was elected MP with a majority of 11,946 and a 52.2% vote share on a turnout of 63.7%. This was a 3% increase on Nick Raynsford's previous majority.
He gave his Maiden Speech in a debate on the economy on 4 June 2015.
In the various elections following Labour's defeat in the 2015 General Election, Pennycook backed Yvette Cooper for Leader, Tom Watson for Deputy Leader and Sadiq Khan as Labour's candidate for Mayor of London.
In July 2015, he became a member of the Energy and Climate Change Select Committee. He was Parliamentary Private Secretary to Shadow Minister of State for Housing, John Healey MP from 2015, resigning from the position in June 2016.
Matthew Pennycook campaigned to remain in the EU during the 2016 referendum and his Greenwich and Woolwich constituency voted 64% to remain. After the referendum majority vote to "Leave", Pennycook was appointed one of the Shadow Ministers for Brexit in October 2016, and, in accordance with the Labour Party whip, voted for the Bill to trigger Article 50.