The authorship of this instrumental is a tangled tale involving transposed labels and titles, with the result that the credit is shared between String-A-Longs members Richard Stephens and Jimmy Torres (the group originally had the endearing name the Leen Teens), and record producer Norman Petty. You can read the full story here. https://en.wikipedia.org/wiki/Wheels_(The_String-A-Longs_song)
It reached No 3 in America in 1961 and No 8 in Britain.
Later that year Joe Loss and His Orchestra took the Wheels Cha Cha to No 21 in Britain. I seem to have a memory of it being played on the wonderful old show Come Dancing, far superior to Strictly Come Dancing.
It was also recorded in 1961 by Billy Vaughn who took it to No 1 in Germany and No 28 in America.