Qureshi was born in Greater Manchester, but he was brought up in Westminster, London, when his parents moved in July 1965. He attended Quintin Kynaston School and graduated from the University of East Anglia with a degree in Development Studies before undertaking an MSc in Environmental Economics at University College London.
Qureshi is of Bangladeshi descent, and comes from a politically active family: his late father Mushtaq Qureshi was a Labour Party councillor in the City of Westminster and was a freedom fighter in the Bangladesh War of Liberation. His youngest sister Papya Qureshi is also a standing councillor in Westminster.
Before becoming an Assembly Member, he worked in Housing and Regeneration for 15 years, helping establish housing associations and co-ops in the East End.
He was an Executive Committee member of SERA from 1994 to 2000 and a former board member of BRAC U.K, an international NGO seeking to alleviate poverty and empower the poor.
Qureshi was a councillor in the City of Westminster from 1998 to 2006, was elected on the Labour Party's party list to the London Assembly in the 2004 Assembly election, was re-elected in the 2008 election and re-elected in 2012 Assembly election. He failed to be re-elected at the 2016 election.
He has been described as "the only Muslim member" of the London Assembly, although he supports Amartya Sen's theory of plural identities and has criticised the practice of individuals "defining themselves simply by their religion, without taking into account other key aspects of their identity".
Qureshi is Chair of the London Assembly's Environment Committee, Member of the Transport Committee. He was a member of the London Fire and Emergency Planning Authority, which oversees the London Fire Brigade between 2004–2012 and Chair of the Mayor's London Waterways Commission, since its inception.
Under his chairmanship of the Environment Committee at the London Assembly a body of work emerged against expansion of Heathrow airport work and its adverse environmental impact on Londoners quality of life particularly in West London subsurbs including reports Plane Speaking (2012) and Flights of Fancy (2010), plus consultation responses on the Government's Draft Aviation Policy Framework (2012) and more recently against night flights.
In "Flights of Fancy" produced before the last general election in May 2010, it argued against Labour government keenness to have a third runway at Heathrow. Since losing the last general election the Labour Party has dropped its expansion of Heathrow airport position.
As an Assembly Member he has undertaken rapporteurships into pedicabs (cycle rickshaws) and the loss of London's playing fields. The latter report called for Sport England to be consulted on all applications for developments on playing fields measuring 0.2 hectares or more, a policy which has since been adopted by the Department for Communities and Local Government.
Among campaigns Qureshi had called for the inclusion of Twenty20 cricket in the 2012 Olympic Games, a proposal which has received the backing of the London Assembly, and he has advocated the use of blue lines to mark the courses of London's underground rivers.
He has called for Edgware Road tube station (Bakerloo Line) to be renamed Church Street Market, as this would end the confusion between that station and the namesake station on the Circle, District and Hammersmith & City lines.
He has worked to raise awareness of the crucial role of remittances in international development with his last letter in the Financial Times generating much debate.
In 2007, Qureshi hosted a meeting at City Hall which launched the Cambridge IGCSEs in Bangladesh, Pakistan and India Studies with Amartya Sen's support.
Qureshi closely follows political developments in South Asia and was in Bangladesh for the parliamentary elections in December 2008.
He is Chairman of Capital SERA, the London branch of SERA.
He contributes regular columns to the China Daily, Tribune and West End Extra.
Qureshi has a music record named after him and has financially backed a British film Shongram, which is a romantic drama, set during the 1971 Bangladesh Liberation struggle.