Simpson was born in Sheffield on the 23rd December 1944. An only child with an absent father, he attended Sheffield Central Technical School. He joined the Amalgamated Engineering Union (AEU) on becoming an apprentice at the age of 15 and worked for Firth Brown Tools until 1966, followed by a long period at the steelmakers, Balfour Darwin, formerly the Arthur Balfour Co. Ltd, from 1966–81. It was there that he became an AEU shop steward in 1967 and shortly afterwards joined the Communist Party. His factory was one of those workplaces to engage in a workplace occupation in the early 1970s and Derek was later the convenor of shop stewards there.
By now a leading light on the influential Sheffield district committee, which was then dominated by Communists, in 1981 he became a full-time union official, becoming the AEU's District Secretary for Sheffield, replacing the, by now, retired George Caborn, and almost legendary Communist predecessor. During all this time, Simpson attracted no controversy over his political position, which remained supportive of the Morning Star, for example.
In 1987, Simpson received an Open University BSc in Computing and Mathematics.
Though his Party involvement was unremarkable, Simpson remained a member of the Communist Party of Great Britain until it disbanded in 1991, never signing up to the re-established Communist Party but joining the Labour Party in 1994, which he has remained a supporter of ever since.
He was obliged by the unfair rules then applying in the AEEU to resign his job in Sheffield so as to be able to stand for the in June 2002 election for the position of General Secretary of the AEEU Section of Amicus, beating the effective incumbent, Sir Ken Jackson. This put him in position to assumed the position of position of Joint General Secretary of the newly formed Amicus and then the sole General Secretary in May 2004 following the departure of the MSF Section's JGS, Roger Lyons.
Unquestionably, Simpson was the left candidate, backed by the Engineering Gazette group of the broad left of the former AEEU, which would soon become Amicus Unity Gazette (AUG). During this election campaign he appeared at fringe meetings of the Amicus MSF section conference in Blackpool, defying an instruction from Jackson not to attend. He was still identified with the AUG, at least formally, until 2008, when he helped launch the rival "Workers Uniting", largely in opposition to the increasing alliance between the T&G Broad Left and the AUG, which led to the formation of United Left, the main current within Unite the union.
Following the merger of Amicus with the Transport and General Workers' Union in 2007, he was (with Tony Woodley) the Joint General Secretary of the biggest union in the UK and Ireland, Unite – the union from 2007 until 2010.
In October 2008, the Executive Council of Unite decided that there had to be an election for the General Secretary (Amicus Section), a ballot just of former Amicus members, with the results to be announced in March 2009 and a fixed term until December 2010. Simpson won re-election but not spectacularly and retired at the age of 66 years, an extension having been agreed in the terms of merger.