As an aspiring barrister, who has completed their LL.B. and the Bar Professional Training Course, I would say that the Bar is fiercely competitive for young up-and-coming lawyers - and will only become more so.
However, I would echo the sentiments that Oxbridge is not the be-all and end-all when it comes to becoming a successful barrister - you do not have to feel like it's "solicitor or nothing". That being said, academic excellence is still quite key. I myself received four A-grades at A Level and then received First Class Honours for my degree at a RG University. In my first year of applying for a pupillage (the 'trainee' stage of becoming a barrister for those unaware) I received 6 first-round interviews and 3 final-round interviews at top London sets, many of which were identified above as being exclusively or, at the very least, heavily Oxbridge. Now, to put that in to perspective, many people undertake an LLB, a Master's perhaps, and the BPTC and spend year after year applying for pupillage (sometimes making upwards of 20 applications a year) and are invited to 0 interviews.
Tl;dr: If you're quite bright - but more importantly dedicated and ambitious - there is no reason why you cannot succeed at the Bar - be it regional or in London.
EDIT: That being said it does require some extensive thought and consideration - aiming for the Bar is a massive commitment (i.e. financially of over £20,000) with no guarantee of success.