I think in an educational context such as this, you simply aren't going to see really high correlations.
There's an old PDF online showing some very old research for medicine looking at interview scores and the MVAT (BMAT precursor).
I think the correlations between interview score and Tripos performance was 0.078. (Although presumably interview score may also be factoring in stuff like "empathy" etc, which isn't tested in Tripos, which will obvs push the correlation down.)
I'll see if I can find the document. It might no longer exist on the internet though...
I think even around 10 years ago, they may not have asked for UMS. And even then, the BMAT hasn't been around that long. Might just have been GCSEs, AS grades, and interview in those days...
EDIT: Found the document:
http://www.cambridgeassessment.org.uk/Images/109717-medical-and-veterinary-admissions-test-validation-study.pdf