 Diveney appeared as series regular Kate Travers in the ITV1 Drama "Injustice" where she played the on-screen daughter of James Purefoy and Dervla Kirwan.She then went on to play Bridget in Bijan Sheibani's production of "Moonlight" at the Donmar Warehouse, where she starred alongside David Bradley and Daniel Mays.Diveney played Julia Masterson in Series 2 of the BBC drama "Call the Midwife", 
In 2014 Diveney starred alongside Sir Tony Robinson and Imogen Stubbs in "The Hypochondriac".