Talk to someone in the department - your potential supervisor, maybe, or the admissions tutor. There's no reason you should have to guess what they're looking for from you; they may even agree to look at a draft and help you to get it as strong as possible. (I got some very useful input from my dept. on my Case for Support.)
I really think a lot of people miss out because they're afraid to ask 'stupid' questions - it's the same story in the seminar room. My advice would always be to just ask! People are usually happy to help and it could make all the difference. I've had quite a dialogue with several people at the dept. I applied to (everything from: is there any 'flab' I could cut in this draft? and, is this specific wording better? to, should I include a 'personal statement'?) - and I ended up being offered this year's departmental studentship.
Obviously you need to be careful not to impose on people - you need to sound them out before you start making assumptions about them having time to read drafts etc. - but certainly don't assume you're on your own.