Is the reputation of the LPC plus masters from BPP any good?Watch this thread
The LPC is fine, they don't really care where you do it. A master's from BPP won't count for anything though. Waste of time and money. You'd be better off getting an LLM at an actual uni and doing the LPC at BPP (or wherever) when you need to (or even just not bothering with the LPC and doing the SQE instead).
You need to first to check if you are under the LPC system or the new SQE system. If the former and you decide not to choose to be within the latter, then BPP is fine but the status of the institution does not matter in the same way it does with your first degree.