Hi @Nanne,
Yes, a very slow-filling cistern is commonly caused by an inlet valve issue. The inlet valve controls how quickly water enters the cistern and shuts off once the correct level is reached. When it becomes partially blocked by sediment or scale, or when it wears internally, water flow can be reduced to a trickle.
In most cases, it is easiest to simply replace the complete inlet valve assembly rather than small internal components. Replacing the valve usually restores normal fill speed and reliable shut-off.
Unfortunately, it looks like you have a back-to-wall toilet seat with a bottom entry inlet valve, which means the inlet valve is connected inside the base of the actual toilet, where you can't access it without shifting the toilet.
Can you see where the inlet hose attaches to your toilet?
Unfortunately, if it is as I suspect, to replace the inlet valve, it seems likely you'll have to contact a plumber for assistance.
Let me know what you find and if you have any further questions.
Jacob
