Both. Some households, usually in older buildings, pay 'water rates' based on the size of their property. Others, including all newly built homes, have water meters which report usage back to the company. We pay for supply of clean water as well as transportation and processing of surface water run-off and sewage.
That's not quite true, water charges are part of your council tax. You get a discount if you have a septic tank because then dealing with the waste water is your responsibility.
But you pay a flat rate based on your property's estimated value in 1991.
In Scotland perhaps. There's no council tax in Northern Ireland either, instead they use the rates system. I'm not aware that there are any discounts for septic tank users.