* Eric Gregory Award for Best First Book of Poems (1985)
* Cholmondeley Award (1985)
* Signal Poetry Award (1990)
* Costa Poetry Award (1998)
* Queen’s Gold Medal for Poetry (2008)
* Bob Marley One World Poetry and Reggae Festival Award (2010)
* PEN Pinter Prize (2011)
* Forward Poetry Prize for Best Collection (2018)
* Lifetime Achievement Award from the BookTrust (2018)
* Lifetime Achievement Award from the Roundhouse (2018)
* Windham-Campbell Literature Prize (2019)