The Open University and the University of Wales Trinity St David's both do distance learning MAs.
Does anyone know which has the best quality teaching?

Does anyone know anything about the Leicester statistics course? Is it better than Southampton? Both universities are roughly as well ranked I think.

If there is a choice of funding bodies are there any that have more 'cachet' than others? e.g. MRC, EPSRC, industry funding - or doesn't it matter?

Research reputations at some non-red brick universities can be very good - depends on the subject. For example Liverpool John Moores is ranked way down the overall academic league but research in sports physiology is top notch (probably even better then Loughborough) as they were the first department to be set up in that subject. So it's horses for courses. There also seems to be a difference in ranking between universities in terms of teaching and research. And some non-red bricks are now cooperating with red bricks - for example at least two are involved in new medical degree courses.