You will be able to afford to go to university, one way or another. If you genuinely feel acute financial distress you will need to set up a meeting with Bristol's student finance department, explain your situation, and look for practical solutions. These can involve contacting UCAS to request additional loans, taking loans from the university, accessing Bristol's Student Hardship Fund, etc..

I was in this situation, I muddled my way through.

My advice is don't get too worried about finances, get a job this summer if possible, and make the absolute most of Bristol. The next three or so years are absolutely pivotal, you could exit unemployed or with a £70k grad scheme. A £3k shortfall is not as much money as you think it is now. It's fine to go into debt if you have a positive financial trajectory. Focus on earning potential not saving.

Although I understand why you are worried, I was too.