I'm not sure I understand, you already have a Bachelors AND a Masters in Business Adminstration, and you want to get another Masters?
Firstly, it seems that you already have the qualifications to get a training contract, now you should focus more on getting relevant experience in my opinion, assuming that you haven't already. I for instance got my training contract straight after my Bachelors degree, but I did have quite a bit of relevant work experience and I also indulged in many extra curricular activities while at university.
I suggest you look at the entry requirements section of the websites for individual firms, and I am sure they will tell you that a 2:1 degree and a decent set of A-Levels will suffice. But if you really want a further degree then I would advise either Manchester or Bath for your masters, although I really don't think you need it.
Secondly, why are you only interested in Ernst & Young? There are many other training firms including the other firms of the Big 4 (PwC, KPMG and Deloitte). Also don't ignore the medium sized firms either such as Grant Thornton, Baker Tilly, BDO Stoy Hayward, RSM Robson Rhodes, Smith & Williamson, Tenon, PKF, Kingston Smith etc which are also EXCELLENT places to get a training contract.