I'm looking for a song called 'Harry' or 'Harry is the one' or 'Harry
is my love' by a a singer called Catherine (I don't know the surname).
 It probably dates from the mid eighties at the latest.

Hello Maggi.

I believe you may be thinking of "Harry" by English singer Catherine Howe.
It was released on an album of the same name in 1975, but apparently has
never been issued on CD.

I found this MIDI file which, although it doesn't have any vocals, should
give you an idea whether it's actually the song you're looking for:

http://www.mcportsmouth.freeserve.co.uk/u/harry.mid


Some very brief information about Ms. Howe comes from the online version of
"The Tapestry of Delights" (a guide to UK bands of the 60s and 70s):

"A folky singer/songwriter... On the Harry album she was backed by members of
 Fairport Convention and she has continued to record throughout the seventies.
 She came from Halifax in West Yorkshire."

http://www.borderlinebooks.com/uk6070s/h11z.html#Catherine Howe


There are several places online which have the LP for sale, as you will find
with the Google search terms:

"catherine howe" harry


Hope this helps you out.
  --brianl