The inlet valve is refilling on its own when the button has not been pressed?
“We have just replaced old inlet valve system with a new inlet valve, which stopped the constant running. Now the inlet valve is randomly refilling on its own when the button has not been pressed?”
It sounds like they are two different problems. The main toilet issues are usually caused by the rubber components, which get worn out over time, especially as they are constantly sitting in water. Your cistern consists of two valves. There is an inlet valve which allows water to enter the tank when the float is in a low position, and which stops the water flow when the float is in the high position. There is also an outlet valve, which allows the water to leave the cistern when the button is flushed. It sounds as though your initial issue could have been a faulty inlet valve, which was not shutting off properly. This would cause the water to constantly enter the tank, exiting via the overflow tube on the outlet valve. If the new inlet valve is running occasionally, it sounds as though you also have an issue with the seating washer on the outlet valve, which may be allowing water to escape. This would cause the inlet valve to refill when the float gets too low. To test this theory, place some toilet paper around the back of the toilet pan (where the water comes through when you flush the toilet). If it starts to get wet, the seating washer of the outlet valve that is not sealing fully. You can purchase new seating washers from most good hardware stores. A new rubber seal is often enough to get an old outlet valve working as new.
