The medieval spelling of Shrewsbury - Scrobbesbrigg (or something similar) did have an "o" in it. I taught at a posh school in Shrewsbury for 25 years, and almost all the pupils pronounced the name as "Shrowesbury",'so I too adopted that pronunciation. That's also the way the name was pronounced by BBC Sports Report football results reader, James Alexander Gordon. Most working class Shrewsbury inhabitants pronounce the town's name as Shoes (like the footwear)bury. That pronunciation, with the "r" added, is a compromise between the two and is often used by people who have little or no connection with the town, a town of which I became extremely fond.
This is great 'scientific' pub crawl analysis from a Professor at University of Shrewsbury, about 15 mins in. I think I might have enjoyed studying there
I believe that the correct (local) pronunciation is "o" and not "ew". It's a bit like Barnsley, we say the hard "a" not the southern soft "a", I hated it when John Dennis used to try to sound posh by saying "Bornsley" like a soft southerner....