When is the best time to apply to unis?

When is the best time to submit application for unis? And when is the latest I should submit my application for best chance of being accepted?
I want to study PPE at LSE/UCL/KCL. The official deadline for these unis are end of January but I'm assuming that it's not optimal to apply close to the deadline unless I'm wrong.

January is the equal consideration deadline - so January is fine, all unis must consider your application equally regardless of whether it is received on 6th September or 15th January (or 31st January if that's the deadline now - I forget )
That said, school deadlines are often before Christmas to allow teachers time to get everything off on time - you should definitely meet your school deadline whenever that is