I got my degree changed from a 2:1 to a 1st on appeal. But I had to appeal based on a technicality (basically I'd had a module deferred to the summer and all the materials from the VLE had been taken offline, making it really hard to complete the work as it was a statistics-based course). The university agreed they'd made a mistake and so pushed my classification up to a 1st, although they didn't remark any of my work so it still says I got 69% on my transcript. It's very difficult to get a classification changed unless you have evidence the university has messed up somehow, even medical evidence isn't usually good enough - they'll just invite you to resubmit the next time the Board of Examiners meet.
Also with things such as depression it's really important you make it known you have issues with your university's disability or support team *before* work is due or you have a bad episode. The more of a paper trail they have about you the more likely they are to take you seriously. I know this is hindsight, but it's my top tip to anyone starting university this September. They have so many people who claim depression after deadlines that if you've got a long history of going to see them, or have even better been assessed for DSA, the process will be far easier.