The map above shows how far out from London you have to go before you get 50% of the UK population (not including the French of course).
The map was created by @election_data who state that:
There so some sensitivity depending on where the line cuts across Birmingham and Bristol but 10km either side of this line gets 49-51% roughly
Moreover, 20% of UK population live within 50 km of London and 33% within 100 km.
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charlie says
Ok. So what is the circles radius please.
Adrian Brown says
Fascinating. From this it follows that if you moved the circle NW to centre on, say, Luton, you ‘d get more than half; and you would therefore make it smaller to get exactly 50%.
Which leads towards what the relevant ‘optimisation’ question would be. How about, Find the smallest possible circle which would enclose precisely 50% of UK population; state its centre and radius?