Just to echo Jantaculum's comments, I also have experience of Cambridge, and it is my impression that it is difficult to pick up full funding once you have already started. Many scholarships, including college ones, specify that you must be about to begin a new course of study in order to be eligible - so current students are excluded if they've already enrolled for the PhD.
From my anecdotal experience, what Jantaculum says rings true. Self-funding students I know managed to pick up some smaller scholarships, grants etc. here and there, but none ever received full funding. There is a preference for giving money to new entrants in order to entice them to come, while with self-funding students, the perception seems to be that since you're already there and the university 'has' you, there's less available. So my view would be that if you enter as a self-funded student, be prepared for it to stay that way - you may pick up some partial funding, but you would be very unusual if you secure full funding after an initial year of paying yourself.
I would also say to be careful about thinking you can rely on things such as college hardship grants (I know you didn't bring them up, but Jantaculum did, so I thought I'd discuss it). Colleges (or at least mine) take a VERY dim view of people attempting to use hardship grants to circumvent the fact that they didn't receive full funding, and you will almost certainly be refused unless you can demonstrate it is genuinely an unexpected financial emergency - simply running out of money because you are self-funded isn't usually sufficient grounds for a hardship grant.
Overall I'd agree with Jantaculum that, for Cambridge at least, you might be better off waiting another year and reapplying if you can, to see if you secure funding the second time round. If you don't, then you're in no worse a position than now, plus if you've worked for a year you might have some savings stashed away which could help if you chose to go down the self-funding route.