There are very few general schemes to secure work experience or mini pupillages at Chambers. Some universities do have them, and some universities have relationships with local sets that can make it easier to secure mini pupillages with them, but on the whole those opportunities are rare. In the main you have to specifically look at the websites of sets that are accessible to you either when you are at university or during breaks/holidays. Each set should have a mini pupillage policy (or at least information) on their website that tells you who they offer mini pupillages to, what they offer (whether the pupillage is 3 or 5 days, whether it is assessed etc), and what you need to do to apply. The goods news is that the vast majority of Chambers offer mini pupillages to under graduates, so there's no reason why you shouldn't be able to find mini pupillages in your first year.
Whether or not you also look at schemes in law firms is up to you. You do seem to be fairly set on the Bar, but there's no harm in gaining broader experience, even if that simply solidifies in your mind that you want to be a barrister. As an aside, as well as mini pupillages there is plenty of other relevant experience you can gain for the Bar specifically, such as marshalling (work experience with a Judge), mooting, getting involved with a law clinic if that is an option, and so on. There's plenty out there if you take the time to look.