If this is something you really want to pursue, I really encourage you to try and undertake a Master's and then reapply. Getting in with a 2ii is going to be very, very tough – possibly nigh on impossible if you can't do the GAMSAT. Your options are limited. Newcastle is a great school, but only offers a couple of dozen places. Compare that to somewhere like Warwick where you have ~175 or so per year.
To answer your question, a post-registration qualification is normally something done whilst in employment; vocational training for nurses who didn't go to university originally, for example.
I understand an MSc is a financially tough option, it's not easy, but if this is what you really want to do then you're going to have to fight for it! Best of luck.