[3] Born in Sheffield to Tamil parents from Sri Lanka[4] in 1970, Rubasingham was educated at Nottingham Girls' High School[5][citation needed], after which she studied drama at Hull University,[6] where she received an honorary doctorate in 2017.

[9] Rubasingham had a long involvement with the international department at the Royal Court Theatre when headed by Elyse Dodgson[10] which allowed her to forge relationships with playwrights from Cuba, Mexico, Brazil, Uganda and India.

[18] The revamped building includes an adaptable stage in the larger 292-seat theatre, better sightlines, new lighting facilities, a new café, improved disabled access and gender-neutral toilets.

[19] During her time as artistic director, her production of Red Velvet by Lolita Chakrabarti was transferred to the West End's Garrick Theatre[20] and St Ann's Warehouse Theater in New York.

[citation needed] Her production of Zadie Smith's The Wife of Willesden has transferred to American Repertory Theatre, Harvard University and Brooklyn Academy of Music.

In August 2014, while she was artistic director, she was at the centre of an antisemitism controversy over the funding of the UK Jewish Film Festival, intended to have been held at the theatre.