Thanks for the pointer, Crayon.
Interesting thread, though not particularly relevant to my situation, which I perhaps should have made clearer in my request.
I am a non-Muslim approaching the age of 50 and so would not, as I understand it, be able to even set foot in Medina or Makkah, let alone (with a cut off age of 25) be accepted at an Islamic university in those cities. Which is fine as I'm looking for a program with a more academic approach.
Two that I have found in my searches are:
Centre for Islamic Studies
Department of Theology, Religious Studies & Islamic Studies, University of Wales, Lampeter
http://www.lamp.ac.uk/cis/CIS_MA_04.htm
Open Study Islamic College
http://www.openstudy.org/?p=index.html
Looking for more like this, in Saudi or elsewhere. Also from anyone with direct experience of the programs above.