Born in Oxfordshire in 1966 Greta grew up in Belgium and Oxford.
She studied Drama at Manchester University and acting at the Ecole Internationale de Théâtre Jacques Lecoq in Paris.
In 1990 Greta returned to the UK where she lived in London for 17 years, co-founding the theatre company Brouhaha. She co-wrote and performed in 3 shows touring UK, Europe and Mexico.
Brouhaha's first show Fish Soup won the Prix d’Or at the Festival de Villard de Lans, France in 1992.
In 1993 Greta began classes with Michael Donaghy at the City University in London.
Over the next few years her poems were published in magazines and newspapers including The Independent, TLS, Poetry Review and The Sunday Times.
In 2001 Anvil Press published her first collection At Home in the Dark which won the Geoffrey Faber Memorial Prize.
Greta began teaching at Morley College in London before going on to teach at Goldsmiths College, University of London. She then become a Poetry Fellow at Warwick University, Writer-in-Residence at Exeter University and Creative Writing tutor at Bath Spa University.
Her second collection Salvation Jane (Anvil) was shortlisted for the 2008 Costa Book Award and her third collection Alive Alive O (Bloodaxe) was shortlisted for the 2016 Roehampton Poetry Prize.
In 2012 her poem Deep Sea Diver was shortlisted for the Forward Prize for Best Individual poem.
Greta's work has been included in several anthologies, most recently Best of British Poetry 2014 (Salt) and Picador Book of Love Poems (2011).
Who’s there? a poem for radio was broadcast on Radio 4's Echo Chamber, was BBC Pick of the Week and shortlisted for the 2017 Ted Hughes Award.
Her short stories have been shortlisted for the 2021 Bridport Short Story Award and longlisted for the 2022 BBC Short Story Award.
In 2022 her fourth collection Fool (Bloodaxe) was published.
In 2023 she received a Cholmondeley Award.
She lives in Devon where she teaches for the Poetry School and the Arvon Foundation.