He was a founding member of German/English avant-pop band Slapp Happy, which later merged briefly with Henry Cow, and has released many solo and collaborative albums.

When he was 14, the Blegvad family moved to England in 1965, unhappy with the social climate of America following the assassination of John F. Kennedy and the threat posed by the Vietnam draft to Peter and his younger brother Kristoffer.

Moore and Blegvad played in various bands during their schooldays, alongside fellow musicians such as Neil Murray (then a drummer, later a well-known hard rock bass guitarist).

Shortly after recording In Praise of Learning, first Moore and then Blegvad left Henry Cow due to incompatibilities with the other musicians in the group.

The album was also notable for its personnel, which included celebrated New York jazz musicians Carla Bley, Michael Mantler, and Andrew Cyrille among the performers.

In 1978, Blegvad reunited with more of his onetime Slapp Happy/Henry Cow colleagues (Chris Cutler, Dagmar Krause and Fred Frith) when he joined the live band for the only tour made by Art Bears.

From 1992 to 1999, The Independent ran Blegvad's strangely surreal comic strip, Leviathan, which received much critical praise for blending some of the most interesting elements of Krazy Kat with a coming-of-age-esque story akin to Calvin and Hobbes.

In 2013 the book was published as Le livre de Leviathan in French and received the "Prix Révélation" at the 41st Angoulême International Comics Festival in 2014.

Blegvad's work for BBC Radio 3 includes numerous "eartoons" for the weekly poetry strand The Verb,[8] and a number of radiophonic dramas with Langham Research Centre and with Iain Chambers.

These include guest+host=ghost,[9] featuring Nick Cave; Use It Or Lose It[10] which won a Radio Academy Award in 2012; Chinoiserie;[11] Eschatology,[12] starring Harriet Walter and Guy Paul; and The Impossible Book (2016).

[13] His 2015 drama with Iain Chambers for Radio Australia, The Eternal Moment[14] starring John Ramm and Emma Powell, was shortlisted for the 2015 Prix Europa.