Well, i applied to the MSc in South Asian Studies - and it required two written pieces. Since I applied in such a scramble, and was far too unorganized to actually initiate writing 4000 words, i just sent in previous material. One, on homosexuality in India, and the other on the political situation in Kashmir.
Poles apart, eh?
Anyhow, I got accepted. So I'm assuming that as long as it's related to the course you're applying for - it shouldn't matter. I hadn't looked at any sample pieces or anything, so what i'd sent in were crude, unedited, non-formatted opinion pieces. No footnotes, no references, no bibliography. Eh.
Im sure there are plenty of people who sent in well structured pieces, and got accepted. Basically, I'm trying to say - there is no set 'what to do what not to do'.
Especially if you're happy with your topic and half way through it, i say don't stress too much