I know LSE for the most parts gives offers out quite late (although some have received offers early on). The problem is, if you send your application in December or January, there is a chance that they may already have given out a few offers, reducing the amount of offers they have left to give out. Roughly what time (month) is it best to send off you application? Mid-October?
Send it when you have checked everything is perfect, yes you may get a reply earlier by applying in October, but many people don't and have months of nervous waiting. An extra few months can give you time for some extra reading to mention on your PS, and if you're anything like me you will probably rewrite it several times. Make sure to get as many people as possible to read your statement, everyone will have different comments / corrections to note; of course you don't necessarily need to take all of them into account.