As far as I'm aware Sheffield and Loughborough have great reputations in terms of engineering (not sure about bioengineering specifically tbh), Exeter I'm not so sure. If I were you I'd further research Exeter. Also, focus on the type of engineering you want to do first, and go with that!
Apparently Sheffield is a great student city, cheap and the uni has new facilities (The Diamond, built 2015) as well as heavy links to industry in Rolls Royce and It's also part of the Russel Group. I think Loughborough is similar as far as industry links and facilities, but it's not part of the Russel Group.
Overall, I don't think you can go wrong with either Sheffield nor Loughborough. Once you get to the top 10-15 unis they're all pretty similar in quality I think.