Sorry OP but none of the school's will have vacancies. They are in the process of allocating next year's places now.
You will have to move and apply to schools, and get on the waiting list. You will then be allocated a place on the list dependant on how you meet the criteria. These are normally:
Distance from school
Attendance at a'feeder' primary
Sibling at the school
There are others, but obviously you will only get in on distance grounds.
So you need to find a school, move literally next to it, apply and then hope there's not people who meet higher priority than you.
I really don't think you are listening to how this works, at many a good state secondary there are children who live in the same road who don't get in as there are others ahead of them in priority order, you will have to look at each school's admissions criteria and ensure you meet them.
Not being here is going to be a massive disadvantage as it is delaying applying.
Can you afford private fees? That may be a better bet as other than with the very selective ones you may have a better chance of a place and proximity to school is less of an issue. And you dict need to be physically here to apply