Turning off the water supply:
The cold water supply is usually found out the front on the street or behind each flat or unit, or sometimes inside the basement or garage. If possible test an outside hose tap to ensure isolation valve from street pressure has indeed closed off the flow. In cases where this flow is reduced but not stopped call your local council as these street stop valves are generally still the property of the city you live in and therefore they will attend to any repair needed to bring flow to zero.
Check cold water taps inside the home to find out if indeed turned off. If off. Now run a hot water tap and see if this hot flow has also stopped at the same time. If the hot water taps are still running it means your hot water system is supplied by a low-pressure header tank. And you have a low-pressure hot water cylinder in a cupboard or the basement or up in the attic below the header tank. Or the cylinder may be an older type with the header tank directly attached to the top of the hot water cylinder. After locating the hot water cylinder check to locate gate valve on the low-pressure cold supply line from the header tank into the bottom of the hot water cylinder. If you find such a valve turn it off anti-clockwise and recheck to ensure hot flow has stopped coming out of hot water taps. If you cannot find such a valve near the hot water cylinder or up beside the header tank just keep the hot water taps running until the header tank either in the roof space or on the roof has drained down through the hot water cylinder. This draining down may take about ten minutes.
However if you discovered that the hot water taps stopped running when the cold water from the street stopped running. Then you either have a mains pressure hot water cylinder operating off street cold pressure. Or you have a cold pressure reducing valve low pressure hot water system installed under the hot water cylinder or up in the attic or on the roof since replacing an older header tank, or fitted as new.
Please Note:
There is sometimes a low-pressure header tank providing the flow of the cold as well as the hot low pressure to all tap ware and shower valves in the house. If you find you have an equal low-pressure hot and cold water supply system. Either locate the tank above you and turn off its out flowing valves to all pipes or simply test cold water supply to this header tank is off from the street pressure or pump if in a rural area. And drain down through the cold taps.
Whatever you will find will fit into one of these events unless you are on bore water brought up by a pump out of the ground or out of a low supply storage tank by way of a cold water pressure pump. In these cases shut off the pump power supply and close off the isolating valve on the inlet or outlet side of the pump. There are also times when a pump is used to build the pressure up to mains pressure in the home or times or when it is used to provide a fast flow into a higher still equal low-pressure header tank or through a pressure-reducing valve under the low pressure cylinder for the hot water system. Sometimes by way of a header tank on a tank stand, or in the attic or on the roof.
Once the water hot and cold has been placed under control to off position it is time to remove the old plumbing fixture.