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 2009 From Trumpet was commissioned by the BBC Proms for the BBC Symphony Orchestra, conducted by Susanna Mälkki.

Recent commissions include On From Four for Psappha, written for the 400thanniversary of Hatfield House, and Leckey, commissioned by the CBSO Youth Orchestra and conducted by Jac van Steen.

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 of three works for the quartet. This piece and an earlier piece, Dance merrily though the park, has been released on CD by clair-obscur. Pieces for individual members include Bench, 2005, for alto sax and piano commissioned for Jan Schulte-Burnert and most recently Crush, 2010, for solo tenor sax 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 released on DVD. Further work in the theatre has followed including songs and sound design working with Laure Salama and companie D.I. with premieres in Paris, et mort d'une parole ordinaire, 2009, and in Corsica, Cas barre, 2010.

He has also worked closely with and had works commissioned for: Sarah Nicolls, piano, Five Night Pieces, 2001, performed, State of the Nation Festival, South Bank; Claire Booth and Bergamo Ensemble, Suburban Nightmares, 2002, Sounds New Festival; Endymion, bee itch, 2002, Simon Bainbridge 50th birthday concert; Zephyr Ensemble of London, Wind Quintet, 2003, Park Lane Group Series; Chroma, 2005, Stand Around, Music Past and Present Series; Milivojevic, accordion, Mis, 2007, Deal Festival; Agon Trio, and this you is what I would sing, 2007, Aldeburgh Festival; Andrew Mason, clarinet, Hornet, 2001, Park Lane Group Series. Hornet was then later reworked in 2004 into a version for clarinet and ensemble for Mark van de Wiel and the London Sinfonietta. In 2007 Psappha premiered Some Variations in Manchester. In 2003 Foskett was invited to The Karol Szymanowski Academy of Music in Katowice as a featured composer for performances of his works. His song Driving, 2009, was recorded by Daniel Norman and Andrew Ball for the NMC songbook.

Foskett has recently finished a new commission for the Agon Trio and theatre collaborations continue with writer Laure Salama with a planned opera based on the story of Olympe de Gouges. Other projects include a new duet for soprano saxophones for Christoph Enzel and songs for soprano and saxophone for Due Voce in France.