LCE was formed by Madeleine Mitchell in 1992, initially at the request of the Vale of Glamorgan Festival, to perform Quatuor pour la fin du temps by Messiaen, going on to perform at the BBC Proms (with Mitchell and Joanna MacGregor's arrangement of Bach, the last of the Art of Fugue)...[2] Their recording of the Messiaen (using their individual names), along with Quatuor pour la Naissance by Krauze , was the widely recommended version of the work for many years.

The LCE gave a concert for the Hall for Cornwall International Series, replacing the Academy of St Martin's Chamber Ensemble at short notice, with pianist Huw Watkins.

LCE's programme with Kyle Horch (saxophone), Madeleine Mitchell (violin) and Nigel Clayton (piano) of jazz inspired music - Gershwin An American in Paris ("in Mitchell's own highly effective arrangement" - The Times), Shostakovitch Jazz Suite and Weill Little Threepenny Music - was performed at St John's Smith Square Americana Season on American Independence Day 2018.

[22] The LCE's director Madeleine Mitchell won a Royal Philharmonic Society Enterprise Award in 2022 for her creative project linking art and music in film, including her Anglo-Russian LCE String Quartet introduced concert programme with the V&A exhibition Fabergé: Romance to Revolution,[23] returning to the V&A for a sold-out concert during the Chanel exhibition, 2023.

[24] They opened Kensington & Chelsea Music Society 2022/23 season in the newly refurbished Leighton House with Quartet no.5 by Joseph Horovitz (in tribute to the composer who died in 2022) and Brahms Clarinet Quintet.