In 1766, when he had already shown considerable talent as a composer, he was taken to England by the wealthy Englishman Sir Peter Beckford, who provided for Clementi's lodging and musical education in return for musical entertainment at his estate in Dorset. It was here that Clementi learned to play the harpsichord. In 1770 he made his public debut as a pianist, and the enormous success of this led to one of the most successful concert pianist careers in early history. He moved to London in 1776, where he performed as a soloist and directed concerts from the keyboard. By 1780 he was considered by many as one of the great keyboard virtuosos of the world, which won him the enmity of Mozart, who described him in a letter to his father Leopold as a charlatan, a mere technician without a scrap of musical talent. A famous piano contest with Mozart in Vienna was declared a draw because of the outstanding qualities of both performers. A successful European tour brought him as far as St. Petersburg.

Mozart's derisive comments may have been partly responsible for Clementi's long neglect. It is now recognized however that, in addition to all his other talents, he was a fine composer, and a key figure in the development of piano building, piano technique, and the sonata form. His works include vocal works and chamber works, a number of symphonies that are fast gaining popularity, a piano concerto, and a large body of piano compositions.

Central to Clementi's piano oeuvre are the over hundred piano sonatas and sonatinas, of which the one called Didone abbandonata is deservedly the most popular. The easier sonatinas are known by every piano student, but the advanced sonatas are often more difficult to play than Mozart's sonatas. Equally important are the three volumes of studies called Gradus ad Parnassum (fondly persiflaged by Debussy in his Children's Corner), and his pedagogical book Introduction to the Art of Playing the Piano Forte.