Here's the response from Bill Caddick:

Hello Tom,

Thanks for the interest. It was a very long time ago but I seem to
remember a black and white TV version of "Hamlet" (this may be fantasy but I think it was actually filmed in Denmark) starring Richard Chamberlain (he of "Dr. Kildare fame in those days) and John o' Dreams was mentioned. I'd already thought of Tchaikovsky's theme from his No. 6 Symphony as a great tune (!) and the two just went together. The melody is "flattened out" a bit but is always recognised as Pete's as far as PRS etc are concerned. Will that do?

Cheers, Bill