Buffini was born in Cheshire to Irish parents, and studied English and Drama at Goldsmiths College, London University (1983–86). She subsequently trained as an actor at the Welsh College of Music and Drama. For Jordan, co-written with Anna Reynolds in 1992, she won a Time Out Award for her performance and Writers' Guild Award for Best Fringe play. Her 1997 play Gabriel was performed at Soho theatre, winning the LWT Plays on Stage award and the Meyer-Whitworth Award. Her 1999 play Silence earned Buffini the Susan Smith Blackburn Prize for best English-language play by a woman. Loveplay followed at the RSC in 2001, then Dinner at the National Theatre in 2003 which transferred to the West End and was nominated for an Olivier Award for Best Comedy.