I live in London but am Swedish and more familiar with that system really, having taught more there (and having done all of my studies there). In Sweden we don't have GRE's and similar tests. We do have a SAT-style test but that's very general and only important for university admissions. I don't think that standardized tests like the ones you mention are important in the UK either.

It'd be interesting to hear if the situation is different in the US. I'd be surprised if professors explicitly tried to train their students to score well on these standardized tests but am not very familar with what it's like in the US.