toilet cistern keeps filling and emptying

Toilet worked perfectly for 5years. For last 8 months have had an escalating problem, which three plumbers have failed to fix. All the following are happening but not every time toilet used.
1. Flushing continues after use.
2. Flushing continues after use if any taps turned on in bathroom during process.
3. Cistern fills and empties without anyone pushing flush button if washer on.
4. Cistern starts to fill and empty on its own when no water being used in house - e.g. at night or when I am out.
I am on a joint water supply- last of 4 houses.
Have listed these problems chronologically as they have started over last 8 months.
Three plumbers have been. First one 'mended' a valve. No good. Second one replaced valve with a Dudley Niagara Dual Flush Flushing Valve. No good. Third fitted a non-return valve. No good.
Sometimes flushing the toilet stops the constant filling and emptying, otherwise it stops of its own accord but that can take hours.
I am getting really worried now as no-one seems to know what is happening. Please can anyone advise? And how do I find a good plumber?

Ask plumber number 4 to fit you a fill valve thats good at dealing with high pressure, such as the Torbeck....it seems like your cistern is constantly over filling, and then allowing the syphon to continually allow the cisten to empty.
John

Get a pressure reducing valve fitted on the incoming main supply. The whole place must be @ very high pressure. And a Fluidmaster valve in WC. Where in UK.?. Get no. 5 in Could be me if it`s E.Sussex

Thanks for the replies so far. Should have said that pressure is low not high according to Yorkshire Water. And I am on a joint supply with 3 other houses.

OK, fit whichever valve you choose - we all have our preferences - and have it adjusted so that the water level stops about 1" from the overflow ..... there is often a mark on the cistern inside to show you how full it needs to be.
John