You can't predict it. Last year for our reception place, there was an initial rush as people who'd applied as a "safety school" gave up their places when they got what they preferred. Then there was a slow trickle of spots becoming available due to life changes like moving for work or getting a spot open up at a school higher up on the preference list.
There are changes at the beginning of the school year, and even beyond. In the end we got our space when a child did not turn up for classes in September.
The big issue tends to be people moving into the zone and pushing you down the list.
I kept calling Wandsworth Council, and they really are very helpful and polite (as well as patient!). I was incredibly grateful when we finally got a spot.