I’m a Londoner and have gone through the process of buying a house ahead of my eldest staring school, with state schools in mind (and I discounted faith schools so distance to school was the only relevant point for me).
Most London boroughs don’t have catchments per se as mentioned by PPs.
Do you have an idea of where you want to live/which state schools you want to consider/try and have a chance of getting into?
The first place I would look is the primary school admissions page on the website of the relevant local authority (or more than one if you’re looking at an area of London where you’re on the border of one or more other boroughs - you can live in one borough and go to school in the one next door, it doesn’t make a difference to how places are allocated).
There you will find information on how offers were made for at least the previous year. Some councils will provide more than one year. If they don’t show here, they will exist, you’ll just have to google for it. This will show you the last distance offered on national offer day (which is mid April each year). That’s the crucial metric as it tells you the furthest distance from the school where a child was offered a place. This metric will vary each year. Some years there will simply be more children applying than others due to national birth rate or the demographic of the time of your local area. Numbers of siblings can also impact (most schools will prioritise siblings of existing pupils over first time applicants, even if you live closer) and other things like new housing in the area near to a school. But if you look at this going back a few years it will give you a sense of the likely distance away from the school you will need to live in order to have a chance of getting a place. There are unfortunately no guarantees!
That’s what I did and then when looking at houses I had a sense of which properties would likely get us into what schools or not. I’d try and buy in an area where you have reasonable back up options. Ie. Not living near an amazing school but likely being offered somewhere you’re not happy with it if things don’t go your way. So don’t have your eggs in one basket.
Councils are very secretive on how they measure distance but a fairly safe bet is to use the straight line tool from google maps between the property and the school. The point on the school is usually the front gate but worth double checking for the schools you are thinking of.
I found this website which is quite helpful:
primaryschoolcatchment.co.uk/
You can plug in a London postcode and it will show you what schools you would have got into in the last couple of years. Such tools are not foolproof. Ie this will show a circle around the school created by the last distance offered metric. You asked about circles and the actual allocation will not look like a circle in reality. It will mean that the furthest away person lived on the outline of that circle if that makes sense.
Also all these figures relate to the first offer day. People living further out who didn’t get a place might end up getting offered one through the wait list systems. Wait lists in London can move more than other parts of the country as people tend to be fairly mobile but again, no guarantees.
This all sounds quite complex but I think if you sit at a laptop with a cup of coffee and read the info from your local authority on the process it will soon make sense to you.
Senior school offers work in a similar way - less of them but bigger in size so usually go out to a wider distance. I looked at these as well as primary as wanted to buy a house where the kids could realistically get into both good local primary and secondary state schools. Ask me again in 6 years and I’ll let you know if it worked!
Sorry for the essay. Good luck.