Not necessarily, because that's not how it works.
You put down your chosen schools on the local authority's form, in your genuine order of preference – ie. the one you want most goes at the top, followed by your second choice, etc. The LA tells every school on your list that you have applied. Each school then tells the LA whether they can give you a place, based on their own criteria (EHCPs, siblings, distance, etc). But, crucially, they don't know what rank you've given them on your list; they only know you're interested.
The LA then goes down your list, starting at the top. If your first choice of school has said yes they'll take you, then that's the one you'll get. If they said no, the LA then checks whether your second choice has said yes, and if so they give you that one. And so on.
Many schools use distance as a criterion, and most primary parents like to be close to their school, so you do often end up with the nearest school. But it also depends on a lot of other factors – whether it's a high birth year, which schools are oversubscribed, etc – so you could go to one further away.