I was just wondering whether the LLM students who undertake the course full-time (or part-time) on campus at UCL/QM are allocated the same readings and examination papers as the students who undertake the course via the external programme? Does anyone know? Thanks.

I can tell you from experience that both programmes are of equal weight and status - I also believe it is much more difficult to do the external programme, since many usually have full-time job and/or family commitments, and do not have the luxury of tutorial/seminars. You get a similar reading list, but it should be remembered that it is a graduate degree, so it is really what you make of it. The reading lists will give you a direction, but both full-time and external student will still be required to do essential and choose recommended readings of their own volition. The exams are of the same standards, but for obvious reasons (because of the way the exams are done for external students - they can be sat anywhere in the world where there is an exam centre) the questions will be different. that is not to say one set of exam questions are easier than anotehr - there is no difference in difficulty. It should also be borne in mind that no-one is trying to catch you out in the exams. It is an opportunity to demonstrate your leaning through the readings.
Hope this helps. You planning on doing it - I highly recommend it as a much better alternative than doing it full time, particularly if you have bills to pay - but it also means you can keep on track with your career and not lose 1-year.