I've been told it doesn't really matter either way, as long as the degree itself is in Psychology. I was looking at the SPS course at Cambridge too, but you do realise that it doesn't actually involve much Psychology? I'm not sure, but it might not be the best path to take to get into Clinical.
Anyway, with unis like Cambridge and Oxford, I believe they always do BAs, even if your course is very scientific, so it won't make any difference in that case.