Not the Strand campus itself nope there are Halls nearby well closest is Stamford Street.
If you mean Strand campus itself it's slightly confusing at the beginning! And since there is no accommodation at Strand can't help you if you mean accommodation
Can't remember when you choose. But i'm in Stamford Street this year and it's costing around £115 a week. It went up by £10 a week last year, so it may go up again next year.
Stamford Street is apartments, you have your bedroom and en-suite thing and then a kitchen shared with up to eight other people. Very friendly place, though - I'm there now and most of my King's friends are from SSA. And you're so close to campus and central London that you spend nothing on transport, which is great.