[21] Primarily a poet, Greenlaw was the author of two pamphlets, The Cost of Getting Lost in Space (1991) and Love from a Foreign City (1992), before her first full-length collection, Night Photograph, was published in 1993 by Faber.

Her work was included in the 1997 Bloodaxe Books anthology Making for Planet Alice: New Women Poets, edited by Maura Dooley, and the same year Greenlaw's second collection, A World Where News Travelled Slowly, was published.

[16][23][24] Publications for which she has written include the London Review of Books, The Guardian and The New Yorker, and in 2019 she was a contributor to A New Divan: A Lyrical Dialogue Between East and West (Gingko Library).

[25][26] Her work draws on her interest in science and scientific enquiry (there were physicists in her family) and covers themes of displacement, loss and belonging.

[29] Her biography notes: "She has written and adapted several dramas for radio, including Virginia Woolf's Night and Day, Hermann Hesse's The Glass Bead Game, and a series on malaria called Five Fever Tales.

Kirkus Reviews summed up her 2007 coming-of-age book, The Importance of Music to Girls, by saying: "The taut, lyric thrum of Greenlaw's prose reflects her poet's skill....Well-written, bewitching and subtly dazzling.

[16] In 1994 she was chosen as one of 20 New Generation Poets, by a jury composed of Melvyn Bragg, Margaret Busby, Vicki Feather, Michael Longley, John Osborne and James Wood.

[35] For her 2001 first novel, Mary George of Allnorthover, Greenlaw won the French Prix du Premier Roman.

[37] Greenlaw appeared as a "talking head" on the BBC documentaries Top of the Pops: The Story of 1976[38] (2011) and The Joy of the Single[39] (2012).