No help at all, of course, but it could easily be either of them. Bob Monkhouse was a comic genius and wrote some dazzlingly clever stuff.
And Des O'Connor, though chiefly known for schmaltzy Max Bygravesy-type songs, also did some masterful comic ditties, such as 'I Can Pack A Suitcase' and many 'list' songs, such as the one about old time movie stars.
As I say, not a lot of help, but good luck in your researches.