Hi! I am a fresh graduate from Sheffield, which is a russel uni. I totally understand your concern and to be very honest, yes it may be hard. Due to circumstances at the time I did my A-levels and covid, I didn't do quite well, achieving ABBD. I did psychology, music, french and maths (which I did badly and got D, and was not included in the decision for my offer). However I got REALLY lucky and got into Sheffield through clearing after being rejected by my firm UCAS choice. I would like to think that my eligibility for contextual offer and personal statement helped me. So I wouldn't say you have 0 chance.
Having a science A-levels helps in some way, especially psychology and understanding scientific research and concepts. I'd talk to Exeter or Southampton's admissions team to check. I would encourage you to try anyways, putting emphasis in your personal statement that you know psychology as a subject field and is interested in psychology. I'm not sure if these are actual grades or predicted, and whether you've started your EPQ, but make it related to psychology if you can. Or you can start off doing a degree in a subject that is related to your A-levels then do a conversion course.
I really wish you good luck since I know how this can cause anxiety. Psychology is actually a great subject to learn and I've loved this subject and ended up with a 2-1!