You might have a problem if you try and apply for schools before you and the children are physically in the country - if places come up they expect you to take them quickly.
I got a Reception place for my DD at our 1st choice school 3 weeks into the first term. I heard on the Thursday morning, had to go and sign the forms on the Friday and they wanted her to start on the Monday - I basically picked her up on the Thursday afternoon from the school she was at and she didn't go back. They had 4 places come up at the same time and all 4 new children started on the Monday.
Regarding school terms, the autumn term runs from early September to just before Christmas with a week off for half-term in the middle. The Christmas holidays are 2 weeks long. Spring term runs from the second week in January till the first week in April with a week for half-term (next week). Then another 2 weeks holiday for Easter. Summer term starts at the end of April until almost the end of July with a week off towards the end of May.
One thing you might not be aware of, is that there are no 'secular' schools in the UK. All schools, by law, must have a "daily act of worship of a broadly Christian nature". What exactly this entails is basically down to the Head - some just talk about being kind to other people etc, others are full on prayers and hymns.
We also have a lot of faith schools - mainly Church of England and Roman Catholic. Getting places at good faith schools involves a lot of jumping through hoops in London - letters from the local vicar/priest are required along with attendance at church at least twice a month for the last 3 years, extra brownie points for doing the flowers etc and in many cases for the RC schools they want baptism before 3 months.
If a faith school would be your kind of thing, it's worth getting your local priest to give you letters detailing the extent of your commitment to the church as this might help any application.
When you're looking at possible schools, look at how their admissions work (not all schools are the same). Generally it's 'Looked After Children' (kids who are in care or who have been adopted from care), then children with a Statement (medical or educational needs that specifies that particular school), then siblings, then distance from the school gate (can be straight line or walking route which will be different). On the local authority website you will be able to see the last distance offered for previous years. Some schools will have large distances, very popular schools could be as little as 150m from the school gate.
This information is very important - some areas can be 'black-holes'... just outside the last-distance-offered for pretty much every school in the area.
Waiting lists don't work on first come first served, it's all done on how you score on the admissions criteria, so if you love a school try and find a property as close as you can to that school as this will move you up the list.