your question sounds kind of strange to me
"How far can you go without attending film school?"
what does it mean. when your target is to win an oscar then filmschool might be not your best option.
but when i ask your question in just a little different way "what does it take to win an oscar?"
then you will quickly see that there is no answer to this question. or maybe the only answer is, if you want to receive an oscar you must work on films. it is like asking what does it take to win the lottery? well at first you must buy a fortune, but other than that you have no influence. so this whole question will not lead us anywhere.
the other question is, does it make sense to visit a filmschool? yes of course it makes sense, what ever type of school we are talking about it makes sense. it is way easier to learn things at school than teaching yourself, school is a great way to network, you get feedback at school, and when you are lucky you get a degree that you can prove that you learned something. so school totally makes sense, it has nothing to do with film.
you american people are in the very unlucky position that you have to pay for your school (we dont have this concept in germany - school (or university) is allways for free). so in my opinion the only real question is, will it pay off to have such an enormous investment to go to a filmschool.
and to answer that you should know what are your expectations? would i pay 100 grand to learn how to make movies? surely not. would i pay 100 grand to get a diploma and to network? maybe yes.
would i pay 100 grand got get entertained for a few years? sure if i have a rich dad
edit
but you are from the UK, i have no clue if you people have to pay for education or not. if enducation it is for free in the UK, then go for it, if not see the above.