It depends on the type of course and the individual university.
If the course is popular and regularly oversubscribed, then it may have a cap on numbers. There could be a cut-off point where no further applications are considered. From what I've seen on TSR, these are likely to be courses such as MBAs and other business/finance related courses. If you're applying to one of these courses, then an early application would give you a greater chance of an offer.
However, many Masters courses recruit throughout the year. Mine accepted applications up to a month before the course start date, but it had a relatively low acceptance rate (I think it gave 1 offer for every 8 applications in my year).