He left in 1757-8 and went to London, where he directed his first joint concert with J.C. Bach in 1764; both men became chamber musicians to Queen Charlotte about this time. The Bach-Abel series, begun in 1765 and comprising 10-15 concerts each year, was given in their own rooms in Hanover Square from 1775.

Abel directed alternate concerts, including many of his own works, often playing himself and introducing performers from Germany and Paris (where he visited regularly). He and Bach also gave concerts elsewhere, including at court. After Bach's death (1782) Abel spent two years in Germany but was active in the 1785-7 series, the Grand Professional Concerts.

Abel was one of the last professional bass violists; his expressive Adagios were especially praised. As a composer he was most prolific in symphonies and overtures (over 40 works), sonatas for two and three instruments, and bass viol pieces. His works, mostly in three movements, are generally genial and energetic but use a rich harmonic style, often unusual phrase-lengths, and melodies of instrumental character.

Abel was one of a long line of musicians. His grandfather Clamor Heinrich (1634-96) was a composer, organist and bass violist who worked at Celle, Hanover and Bremen. His father, Christian Ferdinand (1682-1737), also a bass violist, was a colleague of J.S. Bach at Cöthen, and his elder brother, Leopold August (1718-94), was a violinist at north German courts and composed several instrumental works.

Johann Leopold (1795-1871), a grandson of Carl August, was a pianist and composer who taught music at German courts and later lived in London.