She became an assistant curator at the Institute of Contemporary Arts, under the tutelage of Sandy Nairne, who is a former director of the National Portrait Gallery.

[5] Her first exhibition was Objects and Sculpture in 1981, which included work by artists Bill Woodrow, Richard Deacon, Anish Kapoor and Antony Gormley.

There she co-conceived a new model for the display of the collection and a blueprint for the museum's future program, including the Turbine Hall commissions.

[2] When the Istanbul Biennial’s advisory board unanimously chose Defne Ayas as curator for the event’s 2024 edition, the Istanbul Foundation for Culture and Arts (İKSV) rejected the board’s recommendation and instead appointed Blazwick; at the time of her selection, Blazwick was a serving member of the advisory panel tasked with choosing a curator for the biennial.

Her writings include monographs on Gary Hume (Other Criteria, 2012) and Cornelia Parker (Thames and Hudson, 2013); and contributions to monographs and exhibition catalogues on Hannah Collins, Keith Coventry, Elmgreen and Dragset, Fischli and Weiss, Ceal Floyer, Katharina Fritsch, Roni Horn, Ilya Kabakov, Alex Katz, Paul McCarthy, Cornelia Parker, Annie Ratti, Hannah Starkey, Lawrence Weiner and Rachel Whiteread; and anthologies including Fresh Cream in 2001.

[10] Blazwick chaired the Cultural Strategy Group at London's City Hall, appointed by Mayor Boris Johnson.

[citation needed] She also served on the advisory boards of the Government Art Collection; Sculpture in the City; and the Trafalgar Square Fourth Plinth Commission.

In 2021, she was part of the search committee that helped select Kasia Redzisz and Bernard Blistène as artistic directors of KANAL - Centre Pompidou.

[15] Additional roles include: Blazwick was appointed Officer of the Order of the British Empire (OBE) for services to art in the 2008 New Year Honours.