The water meter will have replaced the stop cock but it will/should have a lever beside it to turn off the water. There is probably another stop cock internally possibly under the sink in the kitchen. The water meter one will turn off from the road and the internal one will turn off if you have a leak indoors. It is also a good idea to have isolating valves on supplies to loos, etc.
It can be a long way down to the meter so take a torch and check as soon as possible as it is important to know where this valve is.