From the Wikipedia entry:
"Stranger on the Shore" is a piece for clarinet written by Acker Bilk for his young daughter and originally named "Jenny" after her. It was subsequently used as the theme tune of a BBC TV drama serial for young people entitled "Stranger on the Shore."
The track, performed by Bilk (as "Mr. Acker Bilk") with backing by the Leon Young String Chorale, was released as a single on Columbia Records in October 1961, with the label of the single openly proclaiming "Theme from the BBC TV Series." The B-side was "Take My Lips". The single became a phenomenal success, topping the NME singles chart and spending nearly a year on the Record Retailer Top 50. It is the UK's biggest-selling instrumental single of all time, and appears fifty-eighth in the official UK list of best-selling singles issued in 2002.
On May 26, 1962, "Stranger on the Shore" became the first British recording to reach number one on the U.S. Billboard Hot 100, but it was quickly followed, on December 22, by The Tornados' "Telstar", another instrumental. After "Telstar", the first British performers topping the U.S. charts were The Beatles, with their first Capitol Records single "I Want to Hold Your Hand". "Stranger on the Shore" was Billboard's Number one single of 1962.
I guess that means Acker, sorry, Mr. Acker Bilk kicked off the British Invasion of the 1960s!
The only decent video I could find of it is this performance in 1988. And it's pretty cheesy at parts - it could be the updated beat or the fact Mr. Acker Bilk has his shirt buttoned down to at least his navel, or the convincing hairpiece. It just lacks that beautiful, haunting, melancholic feeling of the original recording, but it is Mr. Acker Bilk.