OP, the fact is that it doesn't matter what you think that particular flat is worth: it's worth what someone's prepared to pay for it. Sheffield (at least in parts) is very, very expensive, and people pay well 'over the odds' for a decent house/flat in a decent area.
Is there any way you could postpone until after Christmas? The house that @AltheaVestr1t mentioned would be a good buy - decent area, good shops, Endcliffe Park etc.
To be blunt, I wouldn't want to live in Handsworth, Meersbrook, Frechville, Norfolk Park or Gleadless. I can't speak for Walkley or Hillsborough as I have no experience of them.
@AlexanderHalexander 's analysis of Sheffield is good.
I gave up trying to buy there because every single house I wanted to buy went to best and final offers, and all sold for miles over their asking prices. One problem with Sheffield is that the nice areas are invariably also the best school catchment areas, so you can be competing with people who would rather pay more for their houses and not pay school fees. You're also competing against people who would rather pay more for their houses and also pay school fees, so you are talking about people with a very, very large amount of money.
Basically, if you want to live in a part of Sheffield that anyone would really like to live in, with good transport links, you can expect to pay a lot for the privilege.