Thompson was educated at St George's School, Edinburgh, then read English at Oxford and wrote her Ph.D. thesis on Henry James. In the 1980s she played keyboard with rock band The Woodentops.
She has a son and lives in Edinburgh. Her novel Justine was the joint winner of the 1996 James Tait Black Memorial Prize. She has also won a Creative Scotland Award in 2000 and was a Writer in Residence in Shetland.