Eclair was born to British parents in Kuala Lumpur, Malaya where her father, Derek Hargreaves, who served as a lieutenant in the British Army, had been posted in 1952. Eclair returned to England when she was two years old, and she started her education at Queen Mary school, (now King Edward VII and Queen Mary School), Lytham St Annes. Whilst studying at Manchester Polytechnic she was approached to apply for MI5. She appeared in the early 1990s comedy series Packet of Three, as well as the follow-up series Packing Them In. In 1995 she became the first female solo winner of the Edinburgh Festival's Perrier Comedy Award and in 2005 appeared in the singing contest, Comic Relief Does Fame Academy.

On 18 March 2007, she was voted 39th on Channel Four's countdown of the greatest ever stand-up comedians.

Ms Eclair appeared at Derby Playhouse in The Killing of Sister George from 13 September 2008 until 18 October 2008.

As of 13 April 2008 she has left her weekend talk show on LBC 97.3. Her other radio credits include appearing on BBC Radio 4 in the Just a Minute quiz and afternoon plays, various comedy shows on BBC 7 and regularly has covered for Sandi Toksvig on LBC's weekday lunchime chat show (now defunct).

Eclair has appeared on BBC Two's Grumpy Old Women and its various spin-off shows. In 2006, Jenny starred in the stage-show Grumpy Old Women Live! alongside Dillie Keane and Linda Robson. The show was co-written by Eclair and Judith Holder. The spring saw a sell out national tour, June and July a run at the Lyric Theatre in London's West End and the autumn will see another national tour.

However Eclair's success has waned in the latter half of this decade with her middle of the road "lowest common denominator" comedy failing to impress a maturing audience.

Eclair fronts the Food Standards Agency's salt reduction campaign "Salt, is your food full of it?".

Jenny is currently in a long term relationship with Geoff, but she isn't married, having stated that marriages are naff. She has a daughter named Phoebe, to whom she referred during her appearance on Room 101. Phoebe is now attending the University of Oxford.

In 2005, Eclair's recently-completed home in Camberwell, south London, won the Manser Medal for the best one-off house designed by an architect in the UK.