Thank you all for your replies. I can add this:
1. I did a search at www.musipedia.org, using the Parsons code, without result.
2. I found the score of Maguire and Paterson here
It's not the song I have in mind, alas.
3. I tried to find samples of the other named tunes on the Web, without result (yet). So I cannot say whether one of these is indeed the tune I must have heard before.
4. I wrote the tune down in the key of F because I play it in the key of F on my EC. But of course it can be played in another key.
5. I suspect that I've heard before at least the line of the first four bars. However, it's possible that I made up the rest of the tune, as I play it, myself. Hereby the whole tune as I play it.
Greetings to you all!