It honestly completely depends on where you live and what they offer for the most part. Sheffield is a very prestigious university and their CompSci course is very theoretical, most if not all of their applicants come from A level maths backgrounds, so meeting those expectations through an Access course will be very hard.
Have you looked at other universities? KCL for example only ask for 15 credits in maths, all at distinction. I'd also argue that KCL is a better university than Sheffield.
I'm about to complete my Access to HE course in computing, which only makes up 9 credits in maths modules, I have an offer from the University of Nottingham for Computer Science which I am accepting.