I was thinking about this problem overnight. There are several metrics which could be considered (and the considerer not to be considered to be too silly).
One is that which minimizes the person-kilometres traveled. A few people who have to travel a long distance balance a larger number who need only travel a short distance.
Another is that which minimizes the person-expenditure outlay. A few people who must take expensive routes, for example on a ferry or over a toll bridge, balance a larger number who do not need to pay for the infrastructure such as public highways over which they travel.
I have very little idea about the locations which minimize the above metrics. If forced to guess I suspect that the location would be somewhere fairly near Nottingham.