We just moved from the US (Colorado) to London in December with a then 5-year old. He'd just started school in the US in August, and joined Year 1 here in the UK in January after we moved.
Assuming you're talking about public/state schools, some basic info:
Each school has a catchment area -- if you live in a school's catchment area you're eligible to go to that school. Catchment areas can be quirky -- you may live just around the corner from School A and 5 blocks from School B, but you may not be in the catchment for A. Once you find a place/neighborhood, call the schools/councils to find what catchment areas you fall in.
Depending on the catchment area, you apply for the eligible schools. Each school has limited places, so you put down several preferences, and they try to match you as best as they can to your list (taking into account things like distance from home, etc.). So there is no way of knowing for sure ahead of time which school your kid will go to. If they cannot match you to any of your preferred schools they'll place in other schools. For instance, say there are Schools A, B, C, and D that you're eligible for. You like schools A and B, so you only put those down on your list. But A and B are already filled up, so you may get bumped to C or D. This is especially important if you're moving in the middle of a school year (when most of the good schools are filled up).
Because you cannot know for sure which school your kid will go into, it is important to make sure the area has good schools, in case your top preferences are full. A good way to do that is to check the
Ofsted reports. Ofsted is a government agency that inspects and produces reports/scores on all schools. I'd say read more than just the overall score -- the descriptions reveal a lot about what areas the school excels in and what areas the school fails at, something that is not evident in an overall score.
As we found out, you cannot apply for schools before you move. You can only apply once you've moved and have a physical address. It can take 2-4 weeks for them to find a place for your child (especially for mid-year moves), so definitely get that started right away. And check up on them! We submitted the application, and waited to hear from them -- after a week and a half, we called and found out that the application had just been sitting on someone's desk by mistake -- if we hadn't called to check, who knows how long it would have taken.
Note that this was all in London. Not sure if/how things are different in the rest of the UK.