Can I get fibre?

I live in an old concrete tower block (Sheffield S3) my wifi is rubbish!
What are the chances that will ever change ?

It is doable, but may well take some lobbying of landlords/local councillors I suspect. There are providers in Sheffield that would be worth speaking with, as Alt Net’s (Alternative Networks) can be more nimble/creative in how they approach such projects.
I’d get your residents committee together, and start making as much noise as you can. One company that is Sheffield based that you might want to speak with is Pine Media.
Good luck!