Hi there, Julie.
'The Harborne Run', a popular feature of student life in Birmingham for many years, consisted of calling in for a pint at every pub from The Duke of York to the Green Man in a single session, usually on Friday evenings.
One of my daughters was an enthusiastic participant in that particular tradition while at the nearby Med School. She's off on holiday at present and should be back in a few days. Being herself a keen Folkie she may very well have the lyrics you are looking for. We both know local singers and musicians there and I feel sure that, between us, we'll be able to come up with the goods.
Cheers,
Ythanside :-D)