Speaking as a barrister (who went to a comprehensive and not Oxbridge and didn’t have any contacts and got pupillage in my first year of applying - and married to another barrister with same profile) - and sitting on our pupillage committee, you need:
(1) good academics - clear run of excellent GCSEs, A Levels (or equivalents) at least a 2:1 and a VC on the BPTC or a good reason why not and some further study to prove your academics.
(2) commitment - evidence of tirelessly pursuing the Bar, taking part (and being successful) in debating, mooting etc
(3) experience - either paid or unpaid, so marshalling, mini-pupillages, paralegaling, internships, death row project type work etc
(4) perform in interview- so evidence you can answer difficult questions, think on your feet, have charisma!
(5) have a good reason why your applying where you’re applying.
Outside London at least, there is absolutely no need whatsoever to have an Oxbridge degree - it needn’t even be Russell group. You certainly don’t need a leg up, but you do need tenacity and financial backing from parents helps. Apply to the Inns for a scholarship, study the Bar course part time while you work. It’s doable, you just have to want it and be good. Self-awareness is key.