Is it possible to do the ACCA exam without doing the course at a college or uni?

Yep, you can self-study.

You can get the books and learn by yourself or you can do online courses which are cheaper than attending an ACCA education centre.

I have a friend who was working full time for Kemp Chatteris while learning ACCA. He didn't go to uni and decided to go down this route, getting work experience while studying. It took him 10 years to complete all the exams but now he's a tax partner at Deloitte.

Bear in mind this is a very challenging course and it will require a lot of commitment on your behalf if you're doing this privately.

Good luck!