If your toilet (or any tap for that matter) vibrates noisily like a foghorn after the toilet cistern has finished filling (or you shut the tap), there's a really easy fix.
Ours started after we'd had the water turned off a few times, and got to the point where it happened every time for several seconds - not brilliant at 3am!
1) turn the water off using the stopcock under the sink
2) open all the taps in the house
3) get someone to hold down the toilet flush
4) very slowly turn the water back on
5) shut off the downstairs taps
6) shut off the upstairs taps
7) let go of the toilet flush
You should now have a quiet toilet again! The cause is 'pipe hammer' caused by the inbuilt air traps in the house filling with water over time. Without the shock absorbing air in the traps the sudden stopping of the water flow when the toilet finishes filling causes the pipes to vibrate.