Keith was born in 1938, Birmingham, and began piano lessons at the age of seven. He wrote his first tentative pieces at the age of nine and spent much of his practice time experimenting with harmony and improvising.
At fifteen he won a scholarship to the Midland Institute (now known as the Birmingham Conservatoire) where he was quickly invited to join the composition group of Christopher Edmunds, and he went on to win the F.Miller Prize for composition.
At eighteen he moved to Manchester and was promptly offered a place at the Royal Manchester College (now the Royal Northern College). There he became friends with such people as John Ogdon, Rodney Friend, Bryan Lester, John McCabe, Neville Roberts and many other highly gifted musicians.
He studied composition with Thomas B Pitfield and David Freedman and at the end of the year he won the Ascherberg Composition Prize with a set of piano pieces. Two years later he won the more prestigious Edward Hecht Prize and his piece was performed by the Halle Orchestra.