As above, the B will make you a very long shot. If you can get that prediction pulled up to an A you have a fair chance at PPE, although below average GCSEs. You may be able to ameliorate this with strong performance in the TSA.
Assuming you did get the B pulled up to an A, you would likely still be less competitive for economics at Cambridge without A-level Further Maths. Same for LSE (for single honours economics) and quite possibly UCL (for the main economics degree at least; something like PPE or HPE where the economics modules are not taught by the economics department may be more of an option). However of those only LSE is overly focused on GCSEs (LSE really probably not an option at all).
If you are studying outside of the UK (i.e. you are an international student) or in Wales, Scotland, or NI and FM is not available to you, your academic referee should explain this in your reference. If you're in England then FM should be available in all schools via the AMSP so that's a harder sell really...