Macdee 'Pneu-Compact' 6 Litre Cistern problem with water flow not stopping ?

I have a Macdee 'Pneu-compact' 6 litre cistern. It has been working fine for two years now, flushing control works fine, however, after a successful flush the cistern refills, but seems to have a problem filling in that it does not fully stop. As a result a small amount of water continues to trickle into the cistern and eventually it must be exiting the overflow as a slow trickle of water is appearing inside the toilet bowl. The only way of stopping this trickle of water is to very quickly lift the cold water tap of either the sink or bath. I know it sounds odd but this seems to stop the flow of water into the cistern and also stop the water being overflowed into the toilet bowl. Also, after flushing, and refilling the cistern we sometimes hear a high pitch noise in the pipework, and again we have to quickly lift the cold water tap to stop this.

I suspect it's the cistern that's causing this problem. Has anyone encountered anything like this before?.

The plumber that installed our cistern and bathroom worktop (or whatever they are called) kindly did not make a hatch so that we could get easy access to the cistern. Therefore the only access is to undo the toilet flush button and then take the front panel (behind the toilet) off. But the view into the cistern is then restricted, of course.