Tony Woollard studied the cello with David Smith at Surrey University (BA Hons) before gaining a post-graduate scholarship to the Guildhall School of Music and Drama, where he studied with Raphael Wallfisch. He later won a Swiss government scholarship for advanced cello study at the Conservatorio in Switzerland, where he spent four years studying with Robert Cohen.

As a chamber musician Tony has played with the Fitzwilliam String Quartet (including trial), the Alberni quartet (Schubert quintet) and with Robert Cohen at his Charleston Manor Festival. For five years he was a member of the Alba String Quartet. The Albas appeared in many prestigious festivals including Cheltenham, Chichester, City of London and Dublin. They were also selected for 'Fresh' at the South Bank Centre and were Park Lane Group artists. They held a Fellowship at Trinity College of Music where they taught chamber music and gave concerts.

As a soloist Tony gave the Swiss premiere of Robert Saxton's solo sonata live on Swiss radio in January 2007 and the New Zealand premiere in March 2009 as part of the Auckland Fringe Festival. This recital also included works by William Walton, Jonathan Rathbone, Yvonne Parsons and Ivan Hussey and was broadcast live on New Zealand's Classic FM. He has played Elgar, Dvorak, Haydn, Tchaikovsky Rococo Variations, Beethoven Triple and Brahms Double concerti with orchestra and gives recitals of the complete Bach and Britten Suites for solo cello.

Tony was principal cellist with the European Union Chamber Orchestra. Other orchestral commitments also include Irish Camber Orchestra, Northern Sinfonia, Glyndebourne Touring Opera, london Classical Players and Urban Soul Orchestra.