Lindop was born in Liverpool and studied at Wadham College, Oxford, where he read English. After two years of postgraduate research at Wadham and Wolfson Colleges, Oxford, he moved to Chorlton-cum-Hardy, Manchester, where he still lives with his wife, Amanda. He was Professor of Romantic and Early Victorian Studies at the University of Manchester.

As a student at Oxford University, Lindop began writing poetry and working with Michael Schmidt, a fellow undergraduate, to co-edit Carcanet (then a magazine and not a publishing house as it now is).

Lindop is a frequent contributor to the Times Literary Supplement, reviewing poetry, biography, fiction, exhibitions and theatre. He also writes essays and reviews for a range of magazines including The London Magazine, Stand, PN Review, Poetry London and Temenos Academy Review. Lindop held the post of editor at Temenos Academy Review from 2000 to 2003.

When Carcanet Press began publishing pamphlets, Lindop's Against the Sea, was among the earliest ones published. Carcanet Press .

His first full-length collection of poems, Fools' Paradise, was published in 1977. Five other collections have been published since: Tourists (1987), A Prismatic Toy (1991), Selected Poems (2000). Lindop's most recent collection Playing With Fire, was published by Carcanet Press in 2006. Carcanet Press - Playing with Fire.

Lindop wrote a biography of Thomas De Quincey which was published in 1981 as The Opium-Eater: a Life of Thomas De Quincey. He also edited De Quincey's Confessions of an English Opium-Eater and Other Writings for the Oxford World's Classics series in 1985, and was General Editor of The Works of Thomas De Quincey, a 21-volume complete edition of his writings, produced by a team of eleven editors and published in 2000—03.

Sigma Press published Lindop's A Literary Guide to the Lake District in 1993 (second edition, 2005). The guide to the area's literary connections won the Lakeland Book of the Year award in 1994.