Hello
I'm in a pretty similer position as you and it worries me too. I got 3A* 2A 4B and a Distinction*. Although I have never been through the appilcation process I have done some snooping around and it seems to me that Cambridge care more about your predicted grades and UMS score as well as interview to get a well rounded view of the candidate; GCSEs are of little concern in the grand scheme of things. However, having said that a lot of successful applicants are running with 8+ A* under their belt. GCSEs are also proof of early academic achievement and hardwork. But tbh, you can still prove that as long as everything else is spot on; your GCSEs won't be your Achilles' Heel.
Alternativeley, I was planning on having a gap-year in which I would take up a few more extra GCSEs in other interests privately and would try to get a few more A*. As well as this, taking up extra-curriculum qualifications e.g Grade 8 in piano could play an advantage. It could also be done with AS/A levels as well but will cost extra naturally (may need a two-year gap for that). That's just an idea though and im unsure whether that would actually work improving someone's prospects, plus it would cost a fair deal and would mean having to take a year or 2 out. I plan to at least apply (if my grades are good enough haha) and see how fair I get before thinking about that though since it's a big commitment.
Don't take my word for this since i've been looking at websites and blogs etc and we know how reliable they are haha