Allan was born in Leeds and was a pupil of Fanny Waterman before continuing his studies with Deni Matthews, Viktor Merzhanov and Guido Agosti.
He made his debut at the age of ten with the Halle Orchestra under Sir John Barbirolli, and while still in his teens appeared at the Edinburgh Festval with the N.Y.O. and at the Promenade Concerts. At the age of eighteen he became the first British student to study at the Moscow Conservatoire.
In a career spanning fifty years he has played with all the major British orchestras working with famous conductors including Haitink, Solti and Sargent. He has touredwidely abroad, most notably returning to the former Soviet Union – from Archangel to Yerevan.
In the U.K. his impressive list of BBC broadcasts included chamber music with string quartets, piano trios and horn trios as well as numerous solo recitals.
His recordings are equally wide-ranging in repertoire, including concertos with the London Philharmonic, the Elgar and Bridge Piano Quintets with the Coull Quartet and solo discs of Chopin, Mozart and Chabrier.
He currently lives in Bristol.