Pre-treatment
London is built on clay. Clay is impervious to water so flow occurs between seams in clearly defined aquifers. As a result soil filtration is limited.
To rectify this situation, around the well plant Chrysopogon zizanioides also known as Vetiver in concentric rings at 15cm intervals and 15cm (6") between rings. Allow two years for the fine dense roots to descend 5m (16') and overlap. The more rings you plant, the better the filtration.
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
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
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
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.
Vetiver foliage is dense and sharp and will form an effective hedge around your well. It will reach 2m but can be neatly hedged and the clippings used for vermin repellent thatch or mulch.
There are detailed documents on the application of C.zizanioides to well protection as well as riverine and slope stabilisation and phytoremediation (use of plants to rehabilitate contaminated soil or water). Modern applications of well protection can be found in Haiti. I'm pretty sure this is also done in Tonga but damned if I can find anything about it online. It's also widely used to contain contaminants on mine sites.
In an earlier revision of this answer I incorrectly attributed documentation to the UN. In fact it was sponsored by World Bank (see p12).
Risks
C.zizanioides doesn't like frost. It may be necessary to find another plant with similar root characteristics but more suited to lower temperatures.