This.
Take the lid off the cistern and see if you can see water leaking down a vertical pipe.
It it is then you most likely have a leaking inlet valve/seal somewhere in the fill mechanism
Another question for the OP: are you sure there isn't a trap in the bathroom that has dried out, allowing you to hear water running in the sewer? Do you have a bidet that you never use? Are there funny smells in the bathroom?

That bath that you never use (hence the smellI don't know what a trap is
No bidet
No smells
). The trap is the u-bend and relies on water to stop smells from the drains from entering the house. If you only use a shower in a separate enclosure then the water in the bath u-bend can dry out allowing sound and smells to pass along the drain pipe and into the house. I had this at Chateaux Skol but luckily the bath drained into a hopper rather than directly into a soil pipe so no smells but a lot of wind noises (no jokes please!) on breezy nights.No, the tap under the metal lid in your garden or on the pavement in front of your house.You mean the old tap for emergencies, hidden behind the cooker,that won't turn?
No, the tap under the metal lid in your garden or on the pavement in front of your house.