Should I apply to UCL with 4As but no A* predictions?

OP - If your school is like this, in that they don't willingly predict A*s, but you achieved 90% in AS modules, perhaps try and get your referee to mention your attainment it in their statement.

You're still missing the point, we're talking about medicine here; if you have never applied to medicine then I understand how you would make the mistake of assuming that it is similar to other competitive courses, but the admissions process is completely different and you cannot generalise. Yes, they will take contextual factors into account but only regarding competitive requirements, not minimum ones.

I'm not missing the point at all. It doesn't matter whether its medicine or not, the minimum requirement is to achieve A*AA, not to be predicted that. It is down to UCL to determine whether they believe that you are capable of achieving those grades and with 4As at AS you almost certainly are, no matter what the school predicts you.

Oh deary me.
The fact that it is medicine is important, it is treated totally differently from any other application, other courses at RG unis are **** easy to get into by comparison (I should know, my first degree was in something else & it required comparatively no effort to get offers from UCL & everywhere else).
UCL themselves state that for medicine they regard predicted grades as important and that they are used heavily in the admissions process, so I would be wary of assuming that they will give someone the benefit of the doubt/guess that they will achieve the grades if they are not predicted the minimum requirement. It's not impossible, but it's risky.

OP: If you really want to apply to UCL and you got high As/you think you will be able to achieve at least one A*, it would really be best to coax your teachers into predicting you one in either chem or bio; they may be cautious but they do want you to succeed and will understand why you need it if it's an admissions requirement.