I was planning on letting my relationship with my boyfriend (who has anxiety) fizzle out when he goes to uni to avoid as much upset as possible. However, he’s started to mention taking a gap year, which I think is to stay with me, but, I would still break up with him. I don’t feel like relationships are suited for me at this point in my life. I feel way too claustrophobic.
I find it really difficult talking to him about these things because he breaks into tears a lot, and freaks out, whereas, I feel I’m too relaxed, and it makes me feel like a horrible person.
How can I avoid as much upset as possible, so that he has a great time at Uni without worrying about me or us? The caveat is that I want him to understand that I’ve made up my mind, and he can’t change it.
LemonVibe 
You are not responsible for his mental health nor him “having a great time.” He is. All you will do is bring yourself down if you try. You may want to tell him you need a complete break and not try to be friends for a few months. It’s easier to make a complete break on the both of you than to try to stay friends.
I agree with the other advice.
Since he is old enough for university, I’m going to assume that he is an adult. Even if he isn’t, it is not your responsibility to coddle him and keep him sheltered from hurt at the expense of your own feelings. You are half of the relationship with him, and if you aren’t happy in it, you have every right to walk away.
You can tell him as gently as you want. Although you have your own reason for leaving, please remember to listen to him at least so that he doesn’t feel trapped and “unheard” post-breakup. However, if he respects you, he will respect your ultimate decision. If he does all sort of guilting, then he probably has issues with himself more than a break up itself.
Good luck.