The list on the accomodation website of halls is all they offer and doesn't cover first years by a long way. There was a romour going round that Clayhill may be extended.
I know quite a few people who didn't get halls and who are rented, and had very little time, most had from about a month to look, find a place and move in. May be worth speaking with current first years as there will be houses that won't be full next year, and they would know about July time.