His first involvement in a ballet production was with the Royal Ballet, when he played the harpsichord in Frank Martin's Harpsichord Concerto. Choreographer Kenneth MacMillan used this performance as the basis for his ballet Las Hermanas.

In 1973 Wordsworth became assistant conductor to the Royal Ballet's touring orchestra and, in 1974, principal conductor of the Sadlers Wells Royal Ballet. He branched out from his steady job with the Royal Ballet in 1987 to perform orchestral repertoire, while retaining a position as an official guest conductor of the company, becoming its music director in 1990. He conducted the major British orchestras such as the Royal Liverpool Philharmonic Orchestra, the Royal Philharmonic, the Philharmonia, the Ulster Orchestra, the BBC Concert Orchestra, the Hallé Orchestra, the City of Birmingham Symphony Orchestra, and the London Philharmonic Orchestra.

He has conducted abroad, mostly in the Netherlands, Switzerland, and Canada. He was the principal conductor of the BBC Concert Orchestra until 2006, thereafter serving as conductor laureate, and also led the Brighton Philharmonic Orchestra. He is also conductor laureate of the Birmingham Royal Ballet, where he was music director for many years. He held a position as a regular guest conductor of the New Queen's Hall Orchestra, which is a revival, after decades, of what was London's primary orchestra in the late 19th century before the founding of the London Symphony Orchestra. This ensemble is an "authentic instruments" late Romantic orchestra, using the instruments and set-ups of orchestras from the time of Brahms, Elgar, Strauss, and Mahler, recognizing the significant differences between the orchestras of that period and those of today's late 20th and early 21st century orchestras.

Wordsworth has recorded for the HNH records group, on both their main labels, Marco Polo and Naxos, and on other labels as well.