Re-reading this thread I now see that these two tunes have been matched by previous posts here, however...

...I don't usually watch it but yesterday I watched the Last Night of the Proms and thought, I know that tune!!

The Saucy Arethusa

I then thought that it is an O'Carolan tune but having heard over 220 of his tunes over the years I had to do a bit of research to find that it is the tune of:

The Princess Royal played beautifully by Ma´ire Ni´ Chathasaigh & Chris Newman

I also have to admit to an error I make, quite often, by referring to the tune as "Miss MacDermott Roe" instead of "Miss MacDermott". I do it in conversations too, but the reason is that there are eight other O'Carolan tunes with the name "MacDermott Roe" in the titles so I tend to forget that this tune is "Miss MacDermott" (also known as "The Princess Royal").

So, sorry for repeating previous information but it was an ah-ha moment for me yesterday.

BTW, it is one of my favourite O'Carolan tunes, and P.S. just between you and me, I don't really relate to the Morris version(s). Sorry! I like the original way better.