The population center of Great Britain is currently a bit south of Appleby Parva ( http://en.wikipedia.org/wiki/Center_of_population#Great_Britain ), which is roughly halfway between Birmingham and Leicester:
http://maps.google.co.uk/maps?q=Appleby%20Parva.&ie=utf-8&oe=utf-8&a... ozilla:en-GB:official&client=firefox-a&um=1&sa=N&tab=wl
Given Birmingham's such a transport hub as well, it really is the natural location, all other things being equal. (Yes GB is not the whole of the UK, but anyone in NI would be flying anyway, so anywhere with an airport is basically equivalent for them.)
Cost potentially makes things unequal, so I'd suggest when comparing two places at which we can get free accommodation taking the distance to Appleby Parva would be a reasonable metric. Google's walking distance (which should be roughly the as-the-crow-flies distance) puts both Manchester and Oxford at around 71 miles.
Tom