I had what sounds like a similar problem with an older toilet in my house recently - it would emit a load groaning/roaring noise when refilling, along with vibration in the pipes.
I finally tracked the problem down to the two-piece design of the arm that joins the floating ball to the cistern ball valve. On refilling, the small section that butts up against the valve would hammer against it, causing the noise. The rubber washer was also knackered, probably due to age.
I couldn't source a suitable washer, so I replaced the whole cistern ball valve assembly (around a fiver from a local plumbers merchants) and that cured the problem.
it is actually quicker and easier to swap the whole ballvalve, often you can leave the old stem in place and just swap the working assembly..
Identify if the cisstern is fed at mains pressure or from a tank, and observe if your old one is side-fed or bottom fed, and measure it before buying a new valve.
If you like, you can repair the old one later, when you have plenty of time and space to work. You can then keep the repaired one as a spare to swap back later. the cost of a repair kit or a new valve is very small.
You might also like to consider swapping the old-style ballvalve to a Torbeck or other quiet valve. they really are astonishingly quiet.
If your pipes are loose they may vibrate but you can clip them to the wall
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