No, they don't. As far as I know, the admission process at Oxford and Cambridge is a little bit different than in the US. They have several deadlines which means that they compare applications after the first deadline, then wait new applications and compare the new applications and some of the applications sent before the first DL and so on until the all deadlines have passed.
I think that there might be a change that some students which are better than the students admitted in the programs early do not get offer if they send their application in the last cycle..