I am sorry to hear about your position, it must be very frustrating to not get a positive response after you've worked so hard.
You mention that you consider yourself to be anxious; do you think this is possibly coming across at interview? Your CV must be good enough if you've been getting to the interview stage, so perhaps your interview performance is what you need to focus on. Have you asked for feedback following your rejection? Not all places will give it, and if they do it might sting a little, but if they're honest then you can target the areas that you need to improve. If you're anxious during interviews, consider what you're doing to prepare for them (you might feel more relaxed if you feel like you have an answer rehearsed for anything they might throw at you). Consider your body language; make an effort to present yourself as confident even if that's not how you feel.
Your local council/citizens advice bureau might have resources/workshops that you can attend to help give you skills for job searching. Additionally, if finances are starting to be a worry, perhaps consider if you are eligible to receive universal credit while you are searching, as they will also have programs to assist with this.
Either way, I would say it is reasonably common to have not had a job while at university, so I wouldn't worry too much about that. It might be worth contacting the university for any industry connections they may have in fields more closely related to your degree. Remember that even if you dont see a job advertised, there is nothing stopping you from 'cold-approaching' and sending your CV to places anyway.
I understand that getting a paid job is the priority, but in the meantime volunteering at places that give you transferable skills is a great idea. Obviously something like working in a charity shop is directly applicable to other retail work, but you can go further and write about aspects like the role being customer-facing, cash handling, stock management, working as part of a team, time management etc etc on your CV
Best of luck with your search. I hope something comes through for you soon.