- 1990 Winner Flame of Youth Fanfare - British Gas Competition
- 1993 Winner English Song Prize
- 1995 Winner Cobbett & Hurlstone Prize
- 1994 Winner United Music Publishers' Prize
- 1996 Winner Constant and Kit Lambert Award - (Musicians' Livery)
- 1996 Winner Royal Philharmonic Society Composition Prize (link)
- 1998 Winner Masterprize International Composing Competition
- 1998 The Philip Morris Award (The Haemophilia Society)
- 1998 Worshipful Company of Musicians Quincentenary Commission
- 2004 Winner International Composition Competition to Honour Greek Poet Pindar
2005 World Bass Clarinet Convention Composition Competition (Netherlands) for Equipoise for Bass Clarinet and Piano.
Andrew was one of 4 composers to received an Honourable Mention at the culmination of the composing competition of the 1st World Bass Clarinet Competition held in Rotterdam, 21st - 23rd October, 2005. The jury was composed of Klaas de Vries, David Loeb, Klaus Ager and Henri Bok.