Southampton does not reject purely on basis of Access, my friend is doing nursing there and we were on the same access course.
Access courses are a lot tougher than people imagine, lots of assignments, lots of presentations, seminars and a 5000 word project at the end of the course, that was mine, hardly the skive it has been made out to be.
The other thing that needs pointing out is Access courses are not an alternative to A levels, they are there to bridge the gap between college and Uni, hence they gives you relevant skills for Uni, like presentation skills, critical thinking, proper referencing and seminar skills.