BPP is a well known private trainer of accountants (for professional qualifications) and has been established as such for at least 20 years. They seem have expanded into degree courses. Therefore I can confirm as a qualified accountant, it is a well known name in the accountancy profession, and it trains lawyers as well.
However, private universities are a new concept in the UK, and therefore you may need further information. As business degrees (as opposed to Professional Qualifications) are fairly new in the UK, an MBA may be more recognised. However, the London School of Economics offers a MiM (Masters in Management) and that would be recognised anywhere in the world.