I might be missing the point here, but do you mean that you want to apply to UCAS on your own, as opposed to your form being checked, filled in and posted by your school? If you do, then it's perfectly possible. I did this, and there were no problems, but I did have the devil of a time trying to find someone to give me an appropriate and relevent reference. It is easier though when you're applying through school, 'cause you get a lot of help filling in the form and you get nagged about deadlines! Also, (and this is just a thought), won't universities question why you're applying without the help of your school - i.e maybe why you didn't want a reference from them? On second thoughts, perhaps universities might view this as initiative/independent thinking - you never know!
Of course you can do it. I did it. You apply with a paper application. However, a referee is needed to verify your qualifications and to write you a reference.
Um...Your college (probably) has years of experience in this department...shouldn't you leave it to them to judge your application once you've finished it rather than think you can do it on your own?
you haven't told us why you want to, what your subjects etc. without that information i think they came to a valid conclusion - have you ever put through a UCAS application? No. Have your sixth form? Yes, many. I'd say go with experience every time.