Born in the Donegall Pass area of Belfast, Purvis joined the PUP in 1994. She stood for the party in the 1996 Northern Ireland Forum election in Belfast South and then in the 1998 Northern Ireland Assembly election in Belfast South, here taking only 271 votes. She is now the director of the Marie Stopes clinic in Belfast. In November 2014 Bernadette Smyth, founder of the Precious Life organisation, was found guilty of the harassment of Purvis, but the verdict was later quashed.
By 1999, Purvis was the PUP's Spokesperson on Women's Affairs. She took a degree in Women's Studies, Social Policy and Social Anthropology and began working full-time for the party.
Purvis stood in Belfast South in the 2001 UK general election, finishing in sixth place with a total of 1112 votes (2.9%).
In 2006, Purvis was appointed to the Northern Ireland Policing Board. Her appointment was later criticised by the Democratic Unionist Party, because of the PUP's links with the paramilitary Ulster Volunteer Force UVF.
In January 2007, Purvis succeeded the late David Ervine as leader of the PUP and MLA for Belfast East. Commenting on her new role she said:
I am deeply honoured to have been made the leader of the PUP. However this is also tinged with sadness given the huge loss of David. It is a huge challenge to step into this role, especially after the good work he did. But this gives us an opportunity to rebuild and continue to serve working class loyalists and unionist communities.
In her maiden speech in the Assembly she said "As long as there is poverty, and as long as there is inequality in education, health and gender, it will be my duty to articulate the needs of the working and workless classes in East Belfast."
She was re-elected in the constituency at the Assembly election held on 7 March 2007, on the tenth and final round of counting.
In June 2010, Purvis resigned as leader, and as a member, of the PUP because of its relationship with the UVF and the murder of Bobby Moffet which was attributed to that group by the Independent Monitoring Commission.
In the 2011 Assembly election Purvis defended her seat as an independent candidate with PUP leader Brian Ervine running against her. In the end neither candidate was elected and instead the Alliance Party of Northern Ireland gained a second East Belfast seat.