You should find places at several of the schools listed, you shouldn't have to wait till end of August, would be up to you to take up those places or not though, for some schools you would have to wait, it's quite unpredictable.
Houses come up all year round, but I must say there seems a dearth of housing in WSL and W-B at the moment though. Given the fact that you're far more likely to get school places in W-B, I'd be putting that higher than WSL where it's harder to get school places and seems harder to get housing too right now. I'd be trying for school places in W-B and WSP and crossing fingers for getting some in both areas. Anyway, yes you'll find housing in September, but less of it. If you're not going for standard expat 4+ bed with 2+ bathrooms, something more akin to what Belgians live in, then 2 bed houses or apartments shouldn't be too hard to find at any time of year.
If you're coming over in 2 weeks, you might just pull off schools and houses at the same time. For W-B, if you don't mind an apartment, you will be more successful.