LSE Accommodation Advice Needed!!! *pretty urgent

I have just firmed LSE for Law (international student) and now am looking to apply for accommodation. Initially, I really wanted an ensuite (because I heavily preferred a private bathroom) but after seeing that it literally isn't available in any of the convenient housing (apart from Sidney Webb) I decided that I would be fine with a shared bathroom.
Realistically, the only options that are available for accommodation are High Holborn or Carr Saunders Hall and I do very much prefer High Holborn, because it's super close to campus and also I would prefer the style of rooms they have (with it being a shared flat with 4 others) but is obviously considerably more expensive (so i will have to convince my parents). If anyone is living at either of these residences, could you please let me know pros and cons of each (because I think social life also matters a fair amount for me).
I have also looked into some private student accommodation for en-suite rooms, but am worried that it would be very isolating and I won't really get to know people, so if anyone is in private accomm, pls let me know ur experience!!!
also final question, do rooms usually release later during results day or periodically, because that's what it says on the LSE website that rooms often become available. I have joined the mailing list, but I will have to wait and see.
Thanks in advance!!!

Sorry can't answer the first questions but rooms will become available from time to time, I think there will be a lot available on results day as there will be a number of students who don't get the required grades whose rooms will be released

Do you know of anyone who was able to book accommodation on or after results day? I can't find much online on whether this has worked for anyone. Specifically do rooms in bankside ever come up again? Thank you!