Mark Holub, the band's drummer and leader, formed the group in 2003 while studying at Middlesex University. Their debut album, Arboretum, won the Peter Whittingham Jazz Award in 2005. Their second album, Sizewell Tea, followed in 2007. A limited-edition live album was released in 2008. The band's fourth album, Sensible Shoes, was nominated for the 2009 Mercury Prize. Their fifth album, Bring Your Own, was released on 7 February 2011. In 2014, the band released the album The People in Your Neighbourhood and a live vinyl LP The Good Egg. 
- Mark Holub – drums
- Pete Grogan – alto saxophone
- Chris Williams – alto saxophone
- Liran Donin – double bass
- Toby McLaren – keyboards
- Arboretum (2005)
- Sizewell Tea (2007)
- Live (2008)
- Sensible Shoes (2009)
- Bring Your Own (2011)
- The People in Your Neighbourhood (2014)
- The Good Egg (2014) - vinyl and download only
- Lynch, Dave. "Sensible Shoes review". Allmusic. Retrieved 2009-07-22.
- Graham, Stephen (2009-07-21). "Led Bib and The Invisible Nominated For The Mercury". Jazzwise. Retrieved 2009-08-20.
- "Mercury Prize 2009: The nominees". BBC. 2009-07-21. Retrieved 2009-08-20.
- Fordham, John (1 May 2009). "Led Bib: Sensible Shoes". The Guardian. Retrieved 2009-08-14.
- "From Middlesex to Mercury – graduates Led Bib are nominated for top music award" (Press release). Middlesex University. 2009-07-27. Retrieved 2009-09-03.
- "Peter Whittingham Jazz Award". Jazzwise. 2007-03-05. Retrieved 2009-08-20.
- "Led Bib Prepares for Mini-Tour". Jazzwise. 2008-10-22. Retrieved 2009-08-20.
- Nicholson, Stuart (2009-08-16). "Led Bib (Jazz Review)". The Guardian. Guardian News and Media. Retrieved 2009-08-20.
- Smith, Sid (2011-01-31). "Mercury nominated jazz quintet’s latest is a thing of unfettered joy.". BBC Music. Retrieved 2011-04-09.
- Fordham, John (2014-04-17). "Led Bib: The People in Your Neighbourhood – best album yet from British jazz-rockers". Guardian News and Media. Retrieved 2014-05-02.
- Kitching, Sean (2014-04-25). "Led Bib: The People in Your Neighbourhood / The Good Egg". The Quietus. Retrieved 2014-05-02.
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