The English & Welsh admission system for schools is very different to Scotland's.
There are loads of idiosyncrasies and, as said above, you'd need to check with the local council, but basically, how it works for most secondaries is that you apply when the kids are in year 6, (like p5 I think? When they're 10/11, anyway), and you put down your top choices in order of preference. (Typically you get 3 choices, but I believe in London it used to be up to 6).
The school has a set number of spaces are they are allocated to children with priority given to DC in care, siblings of DC already at the school, then to children by distance (within catchment) and then if there are spaces left, again by distance (outside of catchment).
There is no attempt to cater for all the DC in catchment - once the school is full, it's full. Those who didn't get in will be out on the list for their 2nd choice, and 3rd if they don't get into their 2nd, etc.
If they don't get any of their choices the local authority will offer them a space somewhere but it could be quite far away if there is a lot of pressure on places.
That's if you're moving schools at the standard time.
Outside of the standard times, you will be offered a space if there is one.
If the school is full, then the school runs a waiting list, not by the time on the waiting list, but using the criteria above. So, if a space comes up, they'll look at the DC on the list, see if any have priority (because in care or have siblings there or whatever) and if not then it's strictly by distance. So, if you move to on the doorstep of the school, you'll be bumped up the waiting list, even if someone has been waiting ages but lives further away.
If there is no space at your nearby school, the local authority will allocate you a space wherever there is one, which may be some distance away.
This system is further complicated by certain schools having slightly (or very) different admissions procedure because of being a grammar school or a free school, or religious or selective, or specialising (eg in the arts).
Why is this system so complicated? It's a hangover from Thatcher, who pushed the idea of "choice" on the school system.
The other thing that's worth knowing about English & Welsh schools is that the year a child is in, depends on where a child's birthday is in the school year (September to August) not a calendar year like in Scotland. So the oldest in the year are the September born. This might mean your DC being in a higher or lower year than you expect at first glance.