You have a 1st and a reasonably amount of research experience, there's little to suggest you wouldn't be at least considered. You actually seem to have a pretty decent background honestly.
Bear in mind it's entirely possibly the Cardiff one rejected you just because they didn't think you'd fit that particular PhD project (or maybe if you weren't applying for a specific project/studentships, they didn't think you had a clear enough idea of a PhD project to do once you were accepted). That doesn't necessarily mean Cambridge will accept you, but it might be worth making sure you have an idea of what you want to do in the PhD project-wise.