Second that. Sound proofing stuff is very expensive and may not work as well as a bookcase or other stuff put accross that wall. I believe you can get plaster board which has sound deadening in it but this obviously means ripping the wall down to install it.
Always have a look at the small gaps such as round skirting and architraves. Sound transmits very well through small gaps and holes, using decorators caulk will help if there is a problem, or expanding foam if it’s big.
Large heavy wallhangings seem to be recommended sometimes, although we are not in Tudor times so they are not a common choice nowadays.
20cm of solid wood and paper will obviously be very good when you compare it against the alternatives!!