The more I thing of Most Beautiful Leg Of The Mallard (mentioned above), the more I think it would be the perfect song for EFL learners, especially if they are also medical students. And it's a real English trad song, recorded on Voice Of The People and can go on for ever.

You might also try The Twelve Days Of Christmas, especially if you also get them to read the John Julius Norwich take which ends up with solicitors' letters being exchanged in an attempt to prohibit the transportation of vast quantities of livestock.