He was educated at Latymer Upper School and then Cambridge University. After a brief spell as Lecturer in Drama at Glasgow University, he began his career as a freelance playwright in 1975 as writer/researcher with the Belgrade Theatre Coventry in Education team.
His subsequent young people's theatre work includes The Magic Cabbage (Unicorn 1978), Monster (York Theatre Royal 1979) and The Witch of Wapping (Half Moon 1980).
In 1982 and 1983 he was Resident Writer with the Bubble Theatre for whom he wrote Glitterballs and The Rogue's Progress.
Other theatre work includes After Shave (Apollo Theatre 1978), R.I.P Maria Callas (Edinburgh Festival / Hen and Chickens 1992), A working woman (from Zola's L'Assommoir) (West Yorkshire Playhouse 1992) and The Standard Bearer (Man in the Moon 2001). He also collaborated with Jeff Clarke on The Burglar's Opera for Opera della Luna (2004) "stolen from an idea by WS Gilbert with music nicked from Sir Arthur Sullivan".
His first work for television was Claws, filmed by the BBC in 1987, starring Simon Jones and Brenda Blethyn. Wyatt then went on to write two scripts for the science fiction series Doctor Who ... these were Paradise Towers and The Greatest Show in the Galaxy. Both of those serials featured Sylvester McCoy as the Seventh Doctor.His other television credits include scripts for The House of Eliott and Casualty.