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&…
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