I'll use Leeds as an example;
For 2011 entry, every candidate was scored out of 46, pre interview stage.
16 was on Grades, GCSE, AS and Predicted,
24 was on various aspects of personal statement (I think these were motivation, insight, responsibility and extra-curriculur, each worth 6),
and then the last 6 points were on the reference.
To get an interview, you had to get 39/46, there was the possibility of one extra mark if you had got 720 or above on the UKCAT. So out of 47, it was worth 6 at Leeds, which is 12/13% of your application.
I think Leeds' emphasis on the reference is pretty low, that's what I heard from Med students when I visited there, so there you go.