In 1993, Alexander 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 specialised since. Other Sketch shows 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 also 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 Dr. Angela Hunter in the hospital comedy Green Wing.

Alexander contributes to the BBC charity telethon Comic Relief, appearing in 2001 as a judge based on Nicki Chapman in a parody of Popstars, in 2003 as Liza Goddard in a spoof of Blankety Blank, and in 2005 in a Celebrity version of University Challenge.

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, and played Layla Barton in the BBC drama All The Small Things, 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. From 2015 she has starred in the comedy series Marley's Ghosts on Gold.