Redo what the Arthurs did, you can hear it in their song.
1. Lay down your time measure. They only use one, but can be boring. Think about the metre of the song, and translate that into it. As you want to do a trad version of it, keep that basic: a modern version might add an off-beat or something.
2. Now lay down the beat of the song, based on the length of each syllable. All-i-son Gross, tum ti-tum tum. While you're doing this, be sensitive to where the natural pitch of the words is going, you'll start to fiddle with this next.
3. Thinking about what you felt just now, add the pitch. All-i highish, son lower, Gross lowest.
4. That's the carcase. Now you've got to put life into it. Practice it until it's yours.
5. Take it out and see how others react. Test with plenty of rubato to see if the song communicates better one way or another.