Working somewhere and being scapegoated is very, very demoralising, and it sounds like you've absorbed this. Your attitude is defeatist - absolutely not being critical, as it sounds like you've had a very hard time and this is a natural reaction, but you need to work towards getting over this outlook, which is not going to help you. Try to work towards framing your life in broader terms - not thinking in the terms that have been handed to you from your last workplace, but taking a step back and seeing that workplace in the context of your life as a whole.
Ultimately you have the choice of either trying to stay in your current field, either by trying to get a job with your references from your current role, or as pps have said, by doing temp work and getting references from there. Have you actually spoken to your boss/HR people/whoever about what your reference would be like? It might be that they are not going to mention the incident, whatever it is. And if relations with the company are so bad, there doesn't seem any harm in asking. Bear in mind that there have been incidents of people being sued about negative references (for libel) so it may be that they have a company policy of being neutral rather than negative. Worth looking into anyway.
Otherwise, you need to think about what other jobs you can do. This might mean retraining (for which you can get a loan, but obvs only do this if it seems lucrative enough). Or there are some training programmes you don't need a loan for - teach first, accountancy for eg. Retraining will mean that you will be able to put your course tutors down as references. Or you could try getting an entry level role in another organisation and working your way up.
I think it sounds like volunteering or some kind of training would be good for you in the short term -- you need to reframe the narrative of your life somehow. Good luck.