Qureshi's parents came to Glasgow as immigrants in the 1960s, where they raised Qureshi and her six sisters. Her first job was as a trainee employment advice worker, soon after which she realised she wanted to work with minorities.
Qureshi is the executive director of Positive Action in Housing, a Scottish refugee and migrants homelessness and human rights charity that is involved in countering racism and discrimination, particularly in housing. Between 1998 and 2000, Qureshi, together with the prominent human rights lawyerAamer Anwar, helped to campaign on behalf of the family of murdered Indian waiter Surjit Singh Chhokhar. She served on the Lawrence Steering Group and has led campaigns to stop extreme far right groups organising or gaining a platform in Scotland. In 2000, Qureshi talked to the broadcaster Catherine Deveney about her background and motivation for challenging injustice. In September 2005, Qureshi travelled to Albania on a fact-finding mission after taking up the case of the Vucaj children. The children were expelled to Kosovo in two separate dawn raids after living in Glasgow for five years as asylum seekers. Subsequently, she was at the forefront of challenging dawn raids against Scotland's asylum seekers. She called on Scotland's First MinisterJack McConnell to instruct Strathclyde Police not to co-operate with immigration officials who carry out dawn raids. The police, she said, "surely must despise doing the dirty work of the Home Office and the far right". Malcolm ChisholmMSP, Minister for Communities in the Scottish Executive, joined Qureshi in citicising the "heavy-handed" immigration policies,. Chisolm described Qureshi as "a very formidable campaigner and completely dedicated to the rights of minorities." In November 2007, Qureshi took up the case of 13-year-old Meltem Avcil, a 13-year-old Kurdish girl from Doncaster, who began self-harming after being detained with her mother at Yarl's Wood Immigration Removal Centre and about to be deported. Enlisting the support of the actressJuliet Stevenson, Sir Al Aynsley, Children's Commissioner, and journalists at The Independent newspaper, including Natasha Walter, Qureshi ran a campaign across the UK and Europe to secure Meltem and her mother's release. In 2015, at the height of media interest in the Syrian refugee crisis, Qureshi spoke out in a heated debate with Sarah Smith against what she described as the BBC's "doublespeak", giving a searing criticism of the BBC’s constant references to refugees fleeing war and persecution as migrants. Qureshi has been a critic of UK policies on civil liberties, comparing the British Government's attitude towards the threat of homegrown terrorism and the subsequent impact on the Muslim community to the experience of the Irish in 1970s and 1980s Britain. She stated that, "it has been made very clear that the Muslim community should expect to be singled out as potential terrorists. People feel they are being targeted, just like the Irish were by the British in the 1970s and innocent people went to jail. The difference is this time round the names will be Muslim, rather than Irish."
Film work
Qureshi appeared in several films and television dramas, including American Cousins, Buried, The Key, Proof, and the controversial Gas Attack, for which she won a best actress award at the 2001 Cherbourg-Octeville Festival of Irish & British Film.