OK I want to keep things pretty general. Which is the better option for a Phd. A Russell Group Uni without an accredited business school or an ex poly with AACSB accreditation. I have identified a faculty member at each who would be open to working with me. I don't think my grades at UG or masters would get me into a Phd at a really top school, so have discounted that option. I'm self funding.

I have a terrible degree and am a PhD candidate at Edinburgh. What matters is the fit between your research interests and the supervisor's. You cannot overstate how few PhD applicants are already following the current scholarly debate in their topic, and are starting from theoretical issues rather than an empirical domain. 

Other things being equal, pick the supervisor and never the university. Compare their h index on Google Scholar and see what PhD students they have supervised, and where they are. 

What are your goals? 

Thanks for both of your replies. I have a topic I am interested in researching. I am a self employed consultant. The thesis would provide fertile material for my marketing collateral. I am not intending to pursue an academic career although a part time university appointment would certainly be considered. My wife is a doctor  

Oh, just write a book. It's way easier. 

Oh, just write a book. It's way easier. 

Oh, just write a book. It's way easier.