Barrister here. From state school, red brick uni late 1990s. No connections in law whatsoever. Wanted to be a barrister from age 11 and just pursued it.
As the barrister earlier up thread pointed out, chambers’ recruitment processes ignore university. That’s all blind. Most application processes only require you to certify you have met the required access standard of 2:1 in qualifying law degree / diploma, and very competent (or whatever it is now) on Bar Training Course. You don’t get through all the education and be certified as suitable to be a barrister by the Bar Trainers if you don’t meet the basic standard.
More important on Pupillage applications is what goes on the form about him. Academic experience is one thing, but we are all looking for a well rounded individual with experience of doing things. Excellent applications I have seen include people who have worked in bars during uni but have been able to explain how that work fits in with what they’re likely to be doing at the Bar (advocating to clients to do the right thing, or how to improve their lot), people who do altruistic acts (even small ones, etc) while studying, working, etc - shows care, courteousness and organisation. See also people who run scouts / sports teams, grassroots stuff, WI, just actively having an interest in something other than law. The worst applications are all just very dry legal and academic information with no personality. They do not survive the paper sift. So much more important is non- legal work experience and other life experience.
As for making connections and finding out about barrister life (it’s great and gruelling in equal measure) ask careers teacher to get a barrister to come and talk to students - contact the Inns of Court and ask them about their schools outreach stuff. Have a range of barristers come - commercial, human rights (doughty street and garden court chambers are good for that), family, criminal, chancery, court of protection, pi. They all come to talk. Or if part of an academy trust they might arrange a local careers fair and encourage barristers and others to come. If he can organise something like that, that’s do brilliantly on his CV in any career.
Year 11 is probably too young for mini pupillages. Year 13 isn’t, but he must be serious in mini pupillage- and smart. There are no stupid questions, but there are ways of behaving that we see from mini pupils that do not make a good impression. He can now, however, always go and watch barristers at work in his local criminal and county courts. They are generally personable and the court staff should introduce him to them so he can try and form some connections.
Contact local solicitors and get work experience with them - if possible, see if he can sit on on conferences with barristers. If he can do some voluntary work at a local law centre, that’s also fabulous.