Bear in mind that as places like Agnes Jones and Prospect Point are private halls, you can still apply to them whether they're in the accommodation booklet or not. Liverpool uni hadn't placed me up until a week before i arrived which was very scary, and if you know for sure that you want to go to a certain private hall it will probably be a much quicker process to do it privately.
I put prospect point as my first choice, and liverpool told me it had been completely filled up. I then met a girl in freshers week who lived there and told me her flat of six or so people only had three occupied rooms, and the same with the flat upstairs. I think what liverpool meant was that their allowance of rooms from prospect had filled up. If the uni says you cant have any of your choices, its worth calling the hall up and trying to do it separately. I wish I'd known this when i was applying!!