Foskett studied with Edwin Roxburgh and Simon Bainbridge at the Royal College of Music and the Royal Academy of Music respectively. He has been supported by grants from the RVW and the Leverhulme Trusts.
His piece Es gibt einige hohe Wellen was premiered by the London Sinfonietta in 2002 leading to the commissioning of his Violin Concerto for Clio Gould, premiered in 2004 and later released on CD, conducted by Oliver Knussen. In 2004 his solo clarinet piece Hornet was reworked for clarinet and ensemble for Mark van de Wiel and the London Sinfonietta.
In 2009 From Trumpet was commissioned by the BBC Proms for the BBC Symphony Orchestra, conducted by Susanna Mälkki. In 2012 the CBSO Youth Orchestra commissioned and performed Leckey conducted by Jac van Steen at Symphony Hall.
Following on from their performance of Some Variations in 2007, Psappha commissioned On From Four in 2011, written for the 400thanniversary of Hatfield House.
His song Driving, 2009, was recorded by Daniel Norman and Andrew Ball for the NMC songbook.
Since 2000 Foskett has worked in close collaboration with the saxophone quartet clair-obsur, writing six pieces to date for the group and members of. In 2007 clair-obscur premiered Three Pieces for Saxophone Quartet at the Konzerthaus, Berlin, bringing together three of the works for the quartet. This piece and an earlier piece, Dance merrily though the park, have been released on CD by clair-obscur.
Pieces for individual members of the group include Bench, 2005, for alto sax and piano commissioned for Jan Schulte-Burnert and most recently Crush, 2010, for solo tenor saxophone and electronics commissioned by Christoph Enzel. An earlier work, Trying to see more, for soprano saxophone and piano, was written for John Barker and premiered in 2004 at the Park Lane Group Series at the QEH.
Foskett began working in dance in 2000. He has worked widely with the dance company Thresh for a number of years with performances in New York, London and Portugal, culminating in 2008 with a large scale piece, The Absent Lover, which was premiered in Chennai, India. He has also written a full length narrative ballet for the London Children's ballet which was premiered at the Peacock Theatre in London in 2006 and was released on DVD.