Theatre credits include:
- Madame Thénardier – Les Misérables (1992–1994, 1995, 2006–2008 and 2010)
- Widow Corney – Oliver! (1994; original cast)
- Rosie – Mamma Mia! (1999; original cast)
- Mrs. Lovett – Sweeney Todd: The Demon Barber of Fleet Street
- Mrs. Brill – Mary Poppins (2004; original cast, 2009)
- Mrs. Pearce – My Fair Lady (Paris Production 2010)
She has received numerous awards and nominations, winning the 1999 Olivier Award for Best Supporting Actress in a Musical for her performance in Mamma Mia!. She had previously won the award seven years earlier for her portrayal of the character Luce in George Abbott's The Boys from Syracuse.
Galloway can be heard on the cast recordings of Les Misérables 10th Anniversary Concert,Les Misérables 25th Anniversary Concert, Oliver!, Mamma Mia! and Mary Poppins.
Film credits include In Transit, About a Boy, Fierce Creatures and the role of the Foreign Secretary in Johnny English. She appeared in Madame de Sade alongside Judi Dench and Deborah Findlay as Charlotte in 2008.
In what was probably her largest television role, Galloway had a principal role in the fifth series episode of Marple The Pale Horse alongside Julia McKenzie. Her role was Bella Ellis - the town's local witch and cook to Thyrza Grey, (played by Pauline Collins) - who are considered prime suspects at many points during the episode. The episode aired as the first part of the fifth series in the UK in August 2010, for some reason before the fourth series had finished airing.
She also reprised her role as Madame Thénardier in the 2010 25th anniversary concert of Les Misérables at the O2 arena, London in October 2010. This concert is now available on DVD and Blu-ray. She was briefly reunited with her former co-star Alun Armstrong at the end of the performance when he appeared alongside the rest of the original cast of the musical for the finale. She and Armstrong had appeared as the Thénardiers in the 10th Anniversary Concert at the Royal Albert Hall. Galloway also played the character in 2006 Broadway Revival of the show.
Jenny worked at the Watermill Theatre, Bekshire in 1982, returning periodically, to assist stage management, drive the van, and lead sing-alongs.
In 2013 she appeared as Sister Thomas in the Father Brown episode "The Bride of Christ".