Hi OP
We moved from London to Cheshire 12 months ago. DS was part way through Y1 when we moved.
I can talk you through the process we went through, just be aware that there will not be a school place waiting for your child on the day you arrive.........
We are in Cheshire West and Chester so had to follow their process: You can either apply for a school place through your own LEA prior to your move (but the application is not looked at by Cheshire until the day you complete or your rental agreement starts. If your LEA has a backlog, your application will probably be sent to Cheshire after you have moved. Or you can apply direct to Cheshire the day you complete or your rental agreement starts.
We applied to Cheshire direct (online) the day we completed as our London LEA had a backlog of cases (due to so many schools being oversubscribed and high turnover of pupils).
Beware, it may take a few days/weeks for Cheshire to process your application depending on their backlog (especially at busy times eg when next years places are being announced).
The application form asks you to state 3 school preferences. Cheshire call the first one, await a response, if no place they call the 2nd one etc. It can take time for the schools to respond - especially if over a holiday period when there are no admin staff in the school. IMHO this is a daft way of doing things, why not just email all your choices at once?
You can state more than 3 preferences (we put 6!).
So in our case, there were no Y1 places available at our 6 preferences (our 6 nearest schools, we were not picky!) and Cheshire said they would find him the nearest available Y1 place. However, by the time the 6th school replied, a place came up at our first choice. All in all this process from application to being given a place took 6 weeks so I had to keep my DS at home during this time.
This was not a bad thing as we took the time to discover our new surroundings and sort out the house! DS settled into his new school straight away, no issues with being away from school for so long!
Our plan, had DS not got into a local school was to keep him at home and on the waitlist for several local schools until a place came up. We didn't want to send him to the school Cheshire allocated only to have to remove him once a closer place came up.
FYI in our bit of Cheshire, they have the "feeder" school system - each primary feeds into a specific secondary and this gives you an advantage when applying for a place at that secondary - might be worth looking if there are any decent secondary schools and which primaries feed into it.
Sorry for the essay but I wish I'd known more about the bloody process when we moved!
PS Cheshire is great and there is absolutely loads to do for kids, don't worry about that!