I don't know if this is still helpful as you posted two weeks ago, but just in case it is..
I have Depression and Chronic Fatigue Syndrome (and anorexia, although don't really want anything for that since I don't think it affects my studies) and I wasn't sure whether to apply or not as I wasn't sure they could help or whether I needed the help.
I did decide to apply though mostly because I thought it would be useful to apply now in case I do suddenly find myself struggling, rather than wait til I have a problem and then be stuck for what to do.
Regarding the medical evidence, my doctor's office was a lazy inefficient s***hole and took longer than they said they would to do the 'letter' and when they eventually did it, it turned out it wasn't a letter, just a printout of my medical records which they charged me ÂŁ10 for (ÂŁ10 for pressing Ctrl + P!
), but turned out the DSA people were fine with this.
Regarding whether they can help you, you don't have to know at this stage. When you first apply using the form, they'll just send you a letter saying whether you are or are not eligible. Once you have that, (if you are eligible) you'll book a Needs Assessment where they'll ask you more questions about how it affects your study.
I had my needs assessment this morning and was really **** at answering the questions (just things like 'how do you find concentration?'), and confused about whether to accept the support, but the lady was really nice and suggested applying for the few things that would make life easier like a printer/photocopier thing. I felt really guilty though since I felt like 'but other students would have to buy this for themselves, why should I get it for free', and did ask her whether most people with depression or CFS took similar levels of support, and she said that although obvs it varies with an individual's needs most people did take what they were offered just because it's available and it's helpful.