For two points x,y in the plane, define their separation in this metric to be 0 if they are the same point, and |x|+|y| if they are distinct (that is the conventional distance of x from the origin plus the coventional distance of y from the origin).
Anyone who has attempted traveling on the railways in this country will instantly recognise the origin in this interpretation to be London, due the the bad transverse connectivity of our rail network.