Considering I used to get 3-4 cwt from my crop each season, bearing in mind I did not dedicate my whole allotment to potatoes I would say I used around 15%of my allotment for potato growing.
Based on this system you would need around 33.3 million allotments using the same system as I did. Put another way an allotment for every 2 people in the UK (65m at the last census )
If you dedicated the whole plot to potatoes then you would need around 5 million allotments!
How does that sound?