There were almost no effective means of filtration for much of the 19th century and drinking water was easily contaminated with other substances so waterborne diseases like cholera were rife in water supplies, especially in big cities. From the medieval period in England poor people had drunk alcohol to avoid contaminated water (even babies went straight from breast milk to light beer) in the 19th century that continued with lots turning to home-made gin. Wealthy people would have been able to afford supplies of fresh water either brought in in barrels or pumped from uncontaminated springs in the countryside, for poorer people there were water sellers roaming the streets but mostly they just had to take their chances with their nearest water pump.
There were running water supplies from the mid 17th century but they were only for the very richest members of society, the pipes were made of wood and relied solely on gravity so the supply wasn’t that reliable and it could only reach the basement level of a house. In the 1860s pressurised water pipes constructed from metal were introduced so running water could reach higher levels of a house which lead to the development of plumbed in sinks and baths in bathrooms. Hope that answers your question :)