Pre-treatment
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London is built on clay. Around the well plant *Chrysopogon zizanioides* also known as Vetiver in three concentric rings at 15cm intervals and 15cm (6") between rings. Allow two years for the fine dense roots to descend 5m (16') and overlap.

This on its own will substantially protect the well from not only from fecal pathogens but also heavy metal and other inorganic contaminations. However, it is still far from a modern notion of potable.

Settle
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Build a settling tank with four compartments, each overflowing down a pipe to the bottom of the next stage. The bottom of each compartment should steeply taper to a pipe with a dump valve for quick and easy flushing of sediment. 

Filter 
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Build a sand filter. Feed the top, tap the bottom. Water exiting the sand filter will have residual turbidity. A charcoal stage would resolve this but would be an expensive nuisance to maintain. 

Clarify
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There are various options.

 - Centrifuge. On a large scale this could be powered by waterwheel. The centrifuge chamber should have a spiral rill to transport sediment and to capture it when spun down. Output will be less murky and fit for bathing and washing clothes. Goes some way to removing larger pathogens provided the tap is correctly positioned.
 - Fines. Certain clays will clarify. Look up "fines" in the context of wine-making. Not a large scale solution. Does nothing for pathogens.
 - Distil. Expensive but very effective. Use for actual drinking water, not for washing or bathing.
 - Microfiltration. 
   - Charcoal and muslin. Expensive, high maintenance, low throughput, not good enough for pathogens. Does clarify.
   - Filter through a raised sealed garden bed again containing vetiver. This should be long and narrow, to maximise travel through the root mat. Water emerging from 2m (6') of this will be clear and "sweet" and certainly a lot safer to drink than anything else short of distillation or brewing. Very suitable for washing and bathing. For drinking purposes either brew or boil small quantities on demand.