Hodge made her professional stage debut in the Howard Barker play No-One Was Saved at the Traverse Theatre, Edinburgh in 1971. She made her West End debut in Rookery Nook in 1972, and worked with Bob Fosse in 1973 on Pippin. However, when applying for television work she found she had become classed as a theatre actress. Having made the breakthrough in the role of Phyllida (Trant) Erskine-Brown in Rumpole of the Bailey, she found when trying to make the occasional return to theatre work that she had been classed as a television actress.
She co-starred with Dame Judi Dench in the 1995 London revival of Stephen Sondheim's A Little Night Music, at the National Theatre, as Countess Charlotte Malcom. In 2003, Hodge featured in His Dark Materials, one of Nicholas Hytner's early productions as its Artistic Director, her third role on the Olivier Theatre stage.
Hodge is an Honorary Graduate (DLitt) of Brunel University and one of the founder members of the Brunel Club.[12] From 2009 to 2015, she played a comedy role in the BBC sitcom Miranda, as the mother of the eponymous main character. Hodge reprised the role alongside the rest of the cast for the 2017 Royal Variety Performance. In 2012 she toured in Christopher Luscombe's revival of Dandy Dick, starring alongside Nicholas Le Prevost. She is Joint President of Grimsby's Caxton Theatre and a Trustee of LAMDA, her alma mater.
In 2008, she guest-starred in an episode of Hustle within the 4th series, playing the character of Veronica Powell. After the BBC commissioned the show for a 5th series in February 2008, it was planned Hodge would make an additional appearance, however due to on-set filming issues the episode her character would have appeared in was never finished, and subsequently never aired. The release of the 5th series was delayed as a result.
In 2018, Hodge played Ursula, the mother of Liberal MP and party leader Jeremy Thorpe (played by Hugh Grant) in BBC Television's A Very English Scandal.
In April 2021, it was announced that Hodge would play the role of Mrs. Pumphrey in the television series All Creatures Great and Small, taking over from Diana Rigg, who had died the previous year.[13]
Delayed for a year from autumn 2020 due to the Covid-19 pandemic, Hodge was invited by Nigel Havers to star opposite him in Noël Coward's Private Lives, the inaugural production of the Nigel Havers Theatre Company, directed by one of her previous collaborators Christopher Luscombe.