In reply to liamw100:
Have a look at the Norwich to Liverpool train (can't recall who runs it now) as it stops in Sheffield. Whilst at uni I used to book my tickets home as soon as they became available and Manchester to Ely was about £18 return, so should imagine Sheffield to Norwich around the same (plus 10 years of price rises..). It doesn't help with knowing anyone but should take some of the burden off transport issues for solo trips!