ArcheryAnnie - Ok, let's follow through your thought experiment and make it the same as the situation you faced.
Let us suppose that Cornwall issues a limited number of passports each year and prioritises applications from redheads. Their supplementary form is used to determine whether or not your application gets priority. If you fill it in and prove that you are a redhead you get priority. If you don't provide adequate proof of redheadedness you don't get priority. If you don't complete the form you are treated as being non-redheaded. Most years you have no chance of getting a passport if you are not a redhead. However, if there is a shortage of redheaded applicants passports will be issued to non-redheads.
Obviously if you are a redhead your chances of getting a passport are significantly reduced if they won't give you the additional form. However, if you are a non-redhead it makes no difference at all. Your chances are exactly the same as they would have been if you had completed the additional form - low but not entirely non-existent. You can still apply. You have not been prevented from applying. But the fact they prioritise redheads means you have no realistic chance of getting a passport. It is their prioritisation of redheads that means you won't get a passport, not their refusal to give you the form.
I do sympathise with your situation. I'm afraid 40 minute walks to and from school are not uncommon - the government regards anything up to 45 minutes each way as reasonable for primary school children. But it is clearly not the best situation.
However, saying that a school won't allow you to apply is a serious allegation. If true the school could lose its funding. That is why I regard it as important to distinguish between not being allowed to apply at all and being able to apply but with no realistic chance of getting a place.
I accept fully that you had no realistic chance of getting a place. I have never disputed that. This school prioritises Catholic applicants. Most years there are more Catholic applicants than places. Therefore, as a non-Catholic, your chances of getting a place at this school were pretty much non-existent even if you had applied. So I accept that, although you could have applied, it would probably have been wasting a preference had you done so. And, as I have indicated up thread, I am sympathetic to the idea that schools should not be allowed to prioritise on faith grounds although I doubt it will change any time soon as it would cost the government billions of pounds to implement such a policy.
I note that you appear to accuse me of interrogating you in a hostile manner. I think you are confusing me with another poster. I have not asked you any questions at all. I have always assumed you had misunderstood the situation, possibly due to the school misleading you. Looking back I believe my posts were attempting to explain how the system works rather than being hostile to you. My apologies for any offence caused.