Look, I hate to be insensitive when people are getting rejections, but try not to take these rejections too personally.
To those questioning why LSE took XYZ months/weeks to respond to them, it's not because LSE is trying to troll you or play games with you. They were seriously considering your application, and holding on to them so that they could be assessed against other incoming and later applications. They probably thought your applications were strong, but they had to wait to see what the profiles of other later applicants were like.
LSE receives over 2000 law applications and they don't all come at the same time. They have to give fair consideration to all on-time applications (i.e. those who applied in January) so it makes sense that it takes them a while before coming to a decision.