In the UK primary school admission process, does an applicant who applies outside of their borough, to a neighboring borough, have a lower likelihood of admission than a resident of the borough the school resides in? Is this true even if the child lives closer to the school as the crow flies than other children in the same borough do?
The straightforward answer here is yes - priority is always given to the local district. It's not a distance thing, per se, but all to do with catchment area. Each school has a catchment area that they expect children to attend from.
There are high scoring schools that are a cause of parents moving homes just to be within the correct catchment.
And there are exceptions - many fee-paying schools accept people from anywhere, or have a specific set of entry criteria.