What do you mean by "not succeeding"? If by that, you mean not being able to finish the program, then I think you shouldn't worry. They admitted you, so they think you'll be able to finish. I've no idea how many people in their class get first year funding, but I would imagine there to be a few self-funded students. Of course if by succeeding you mean getting a good academic placement, then it all depends on your research and where you think you'll be able to do your best. In addition, I think having someone well-known in their field (e.g. Andrew Harvey) as your advisor does help.
While Cambridge may not have had the best academic placements lately, I believe they still place very well at research institutions such as the IMF/World Bank.