In 2009 Sweet won The Edinburgh Comedy Award for best newcomer for his show ‘Mostly About Arthur’. He also starred in Tom Basden’s debut play Party alongside Basden himself, 2009 Edinburgh Comedy Award winner Tim Key, Anna Crilly, Katy Wix and Nick Mohammed. The play won a Fringe First before travelling to the Sydney Arts Festival and appearing in London’s West End and in adaptation as a BBC Radio 4 sitcom.

Sweet became known for playing posh characters after his role as future Prime Minister David Cameron in the 2009 More 4 satirical show When Boris Met Dave, which details how Cameron and Mayor of London Boris Johnson first met. He also appeared alongside Alistair McGowan, Adrian Edmonson and Hugh Dennis in Pete and Dud: The Lost Sketches, a revival of Peter Cook and Dudley Moore’s works on BBC Two.

In 2012, he had a small role in BBC’s Him & Her as one of Paul’s newly found relatives.

He has recorded two series of his Radio 4 sitcom, Hard to Tell, a romance , starring Charlotte Ritchie as his love interest. The structure mainly consists of conversation between Tom (Sweet) and his sister Maeve (Katy Wix) telling his side of the developing romance, and between Ellen (Ritchie) and best friend Hermione (Sarah Solomani). In 2013, he was nominated for the Best Breakthrough Artist at the British Comedy Awards.

In 2014 Sweet starred as Tom Oliver in the Channel 4 police comedy-drama series Babylon. In 2015, Sweet created, wrote and starred in the BBC sitcom Together based loosely on his radio series Hard to Tell. He also wrote an episode of Tom Basden’s E4 series Gap Year.