In 1992, Alexander appeared in
The Bill, as a witness to an attempted robbery. The following year she played Muriel in an episode of the
BBC comedy-drama
Lovejoy. In 1994, she played Nicky, Damien's risk-addicted weather reporter girlfriend in
Drop the Dead Donkey. In 1996, she played Beatrice in the British première of
Octavio Paz's only play, ''
Rappaccini's Daughter, at the Gate Theatre Studio. She has appeared in other theatre productions, including The Vagina Monologues, Hand in Hand
, The Secretary Bird
, Northanger Abbey, and as Lady Macbeth in Macbeth. In the mid-1990s, she met Ben Miller when they filmed an advertisement for disposable cameras together, and through him she met Alexander Armstrong. Miller and Armstrong became friends and collaborators, and Alexander went on to appear on their Channel 4 sketch show Armstrong and Miller'' (1997–2001), usually in the regular "Nude Practice" segment. Alexander moved into comedy acting, in which she has since specialised. Her other sketch show work included
Smith and Jones (1997–1998) and
Smack the Pony (1999–2003), also writing for the latter. In the science-fiction comedy series
Red Dwarf, she played the Queen of Camelot in "
Stoke Me a Clipper". She appeared in the
Midsomer Murders episode "The Garden of Death", as Fliss Inkpen-Thomas. In 2000, she appeared in the comedy
The Strangerers, as well as becoming co-host of the final series of the current-affairs satire ''
The 11 O'Clock Show, alongside Jon Holmes. She made her debut as Susan Walker in the BBC sitcom Coupling, which ran for four series from 2000 to 2004. Other British TV roles included Mel in The Worst Week of My Life and Angela Hunter in the hospital comedy Green Wing''. Alexander appeared as Alice Fletcher in
NBC's short-lived remake of the British comedy series
Teachers, before roles in the films
I Could Never Be Your Woman and
Stardust (both released in 2007). Her previous film credits include
Seaview Knights (1994) and
Going Off Big Time (2000). She also starred in the 2008 BBC
dramedy Mutual Friends, which debuted in 2009. Since 2011, she has played Mimi in the
BBC Radio 4 comedy series
The Gobetweenies. The first series was broadcast in 2011 and two more followed in 2012 and 2013. She starred in the 2012 BBC series
Me and Mrs Jones. Since 2013, she has starred in the
BBC One series
Jonathan Creek as Polly Creek, wife of main character Jonathan, making her first appearance in the episode titled "The Clue of the Savant's Thumb" in 2013. She starred in the Dave comedy
Undercover as DS Zoe Keller. In 2015–2016 she starred in the comedy series ''
Marley's Ghosts on Gold. In 2019, she appeared as Undine Thwaite in the Epix series Pennyworth''. ==Other work==