I just wanted to say that myself and I’m sure many other people on here didn’t go to university so it’s more than possible. You’d probably find exactly the same challenges post university as you will now but it’s just about getting that ball rolling and getting that first foot in the door.
So, do you have any inkling at all of what part of film/ tv you’d like to get into? Perhaps you have an interest in cameras, writing, acting, hair& make up? I personally knew that I wanted to work in the technical side and managed to somehow get a junior job in shopping TV. If you don’t know then that’s not a problem, with some work experience I’m sure you’ll see all the different opportunities and be inspired.
I think you’re doing the right thing by looking for apprenticeships or internships and or even the odd day running here and there just to experience the industry and hopefully you’ll find your calling.