Hello! I'm a current first year law student. I'm in a studio in uni halls. In regard to private halls, there should be quite a few first years due to uni halls costing more than private. However, I believe some private halls require a guarantor so if that's an issue, uni halls are a better option.
Personally I found that I haven't been too isolated whilst in a uni halls studio. The halls often put on social events to allow residents to get to know eachother. The uni itself has a lot of societies so even if you don't get along too well with others in your accommodation, I've found that the societies are great for getting to know new people.
My personal take was that I'd prefer to be in a studio incase I got put in the same shared accommodation as people I didn't get along with. If you're in uni halls, you'll be sharing with other first years I believe. However, I think if you're sharing in private halls, you can get put with people in other years.
Hopefully you're able to decide what works best for you though : )