Can an Access to HE diploma genuinely get me to these universities for these degrees?

So I'll be starting an Access to HE diploma in Business from September 2016. I've been calling universities getting answers to my questions, and I've pinned down the following four degrees I want to apply for, using the same personal statement:


KCL - 'Business Management', N200, 39 distinctions and 6 merits needed

Manchester - 'Management (Accounting and Finance)', NN24, 30 distinctions and 15 merits needed

Durham - 'Business and Management', N201, 30 distinctions and 15 merits needed

Nottingham - 'Finance, Accounting and Management', NN34, 30 distinctions and 15 merits needed


I have two questions:
A) Can an Access to HE diploma genuinely get me to these degrees? The universities I've called and they've all said they would, but I'm still slightly worried and skeptical because entry is competitive (I did have AAB offers from Manchester for Accounting and Finance and Nottingham for Finance, Accounting and Management last year, with ABDE at AS-level done at a private school and not the best of personal statements, which I have improved recently in my own time, but sadly I didn't sit my A2s last year because of a lot of overwhelming over thinking).

B) Would a Business and Management/Management personal statement be acceptable for 'Finance, Accounting and Management' at Nottingham? Or would I need to make sure the personal statement does involve talking points on Finance in it, if NN34 is more of a Finance degree?

AAB for KCL? Really? I thought Business Management was an A*AA course, hence how they ask for 39 distinctions on an Access course, unless you're talking about another degree at KCL?