In early 1981, Poppy co-founded The Lost Jockey, a large ensemble that delved into musical techniques inspired by the works of Philip Glass, Steve Reich, and Louis Andriessen. As a pianist and composer for the group, he created several pieces, including "The Object is a Hungry Wolf."

By the mid-1980s, Poppy had signed with ZTT Records, a label established by Paul Morley and Trevor Horn. Embracing a post-minimal aesthetic within the pop music context, he recorded two CDs. His album "Alphabed" integrated traditional composition with studio production methods, utilizing sequencers, samples, and electronic keyboards, and featured a diverse range of vocalists, such as Annette Peacock, Ashley Slater, Udo Scheuerpflug, and Dee Lewis.

Throughout the 1980s, Poppy collaborated on experimental and visual theatre projects produced by The Institute of Contemporary Art in London, including works like Secret Gardens and Midday Sun. This interest evolved into music theatre and chamber opera, leading to compositions such as The Songs of the Claypeople for Impact Theatre and The Uranium Miners Radio Orchestra Play Scene's From Salome's Revenge for the Royal Opera House's Garden Venture. In 1991, he was commissioned by The National Theatre Studio to create Baby Doll, a chamber opera for three voices based on a screenplay by Tennessee Williams, and in 1996, he composed and recorded Ophelia/Ophelia.

The 1990s marked a resurgence of interest in concert music for Poppy, resulting in works such as 14 Poem and Toccatas for violin and piano, performed at the Huddersfield Festival by Andrew Ball and Elizabeth Perry, and Ember: String Quartet for The Balanescu Quartet. He received commissions for Eight Movements for Piano Trio, Eleven Word Title, Sprung and Suspended, and End Synch Sound (accompanied by a film) from various chamber ensembles. In 1997, the Royal Liverpool Philharmonic Orchestra commissioned Horn Horn, a concerto for two alto saxophones and orchestra. More recently, pianist Jed Distler from New York and UK-based Tania Chen have performed selections from Fruits and Shavings, a collection of 23 pieces for solo piano. The year 2000 saw the release of the CD Time At Rest Devouring Its Secret, a 35-minute studio work that again linked minimalist musical techniques to imagery from popular culture.

Over the past two decades, Poppy has collaborated in the studio with bands such as The The, Erasure, and Nitzer Ebb, and has composed theatre scores for Julia Bardsley’s productions of Macbeth and Family Reunion, as well as Kenneth Branagh’s performance in Coriolanus. His music has inspired choreographers, including Ian Spink, Sally Owen, Michael Clark, Gaby Agis, Sue Davies, Linda Gaudreau, Julia Bardsley, Michael Popper, David Massingham, and most recently, Heidi Latsky from New York. Additionally, Poppy has created music for television and film, notably working with Portuguese director and producer Vitor Gonçalves, and served as head of music at the National Film and TV School in the UK from 1995 to 1997.