He is well known for playing Germanicus in the famous 1976 BBC production of I, Claudius,[4] and as Robin Grant, one of the principal characters in Thames Television's 1981 series The Flame Trees of Thika.
Robb had his big break playing Andrew Fraser MP in the TV miniseries First Among Equals a 1986 adaptation of the book of the same name by Jeffrey Archer.
The miniseries was a great success on prime time TV in the UK and abroad and also propelled careers of co-stars Tom Wilkinson, Jeremy Child and James Faulkner.
In 2020, BBC Radio 4 Extra rebroadcast his performance from 1985 in E Phillips Oppenheim's mystery thriller The Great Impersonation.
Robb performed in two of Richard Norton-Taylor's Tricycle Tribunal Plays: The Colour of Justice (the dramatised version of the Sir William Macpherson inquiry into the murder of Stephen Lawrence, his family's search for justice, and endemic racism in British police forces), and Half the Picture (a distillation of the Scott Inquiry into Arms-to-Iraq.