Access to clean water has always been a major public health problem-- historically diarrheal disease was almost always a major killer, particularly of young children. The more densely populated the area, the greater the problem of water contamination, due to more human waste. The Romans had excellent civic hygiene, bringing clean water into the cities, and segregating waste-- these technologies were present in Roman Britain, the massive stone sewers of Colchester and York survive to this day. It's quite likely some of these Roman facilities remained in use in Anglo-Saxon times, but others would have fallen into disuse.
We have evidence from contemporary texts, including the celebrated medical text "Bald's Leechbook" (compiled in the mid 9th century) that dysentery was a constant problem:
The attention given to dysentery indicates that it also was a common ailment. This was to be expected in a community where inadequate attention was paid to cleanliness of food and water-supplies. Exposure of food and human faeces to flies, contamination of water-supplies by human faecal wastes, handling of food by human carriers who were infected but not necessarily displaying any symptoms and who were careless of personal hygiene, would all have contributed to the spread of the causative agent, Entamoeba histolytica
Wells existed, although note that in Anglo-Saxon usage the term "wella" applies to what we'd call "springs"; so when you see it in a place name like "Wells Cathedral"-- they're talking about natural water sources, not an artesian well. We don't have a lot of examples of pre-conquest dug wells, but we do have some, for example the timber lined Saxon wells that have been excavated at North Elmham
Populations everywhere-- including Anglo Saxon Britain-- settle near water sources. Consider the five largest towns of the time:
City :: Approximate Population :: River
London, 10,000; River Thames
Winchester, 6,000; River Itchen
York, 5,000; River Ouse
Norwich, 5,000; River Wensum
Lincoln, 5,000; River Witham
Access to water: there were established "water rights", but access to drinking water would be less contentious than other kinds of rights and obligations-- such as fishponds, maintenance of drainage canals, weirs and dams.
References:
Finds from a Roman Sewer System and an Adjacent Building in Church Street [York]
The Domesday Book -- a kind of census taken after the Norman conquest-- gives us a pretty good idea of population as of the late 11th century; demographics would likely be changed somewhat from pre conquest, but they're the best data we have
Middle Saxon and Late Saxon settlement, North Elmham Park
Bald's "Leechbook": its sources and their use in its compilation