Don't expect to be in hall accomodation after the first year. There is 0% chance of getting accepted by university accommodation outside of the LSE, even in the first year (bar intercollegiate halls).
The only exceptions to this rule are if you are elected into the hall committee, but I wouldn't count on this, and it only gives you 1 extra year anyway.
Long story short, you need to find accommodation for the 2nd and 3rd years.
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