Good afternoon, Adrian. Music box dampers have been primarily crafted
from synthetic materials for probably six decades; currently Mylar is
used.  We craft such dampers for use in all of our Reuge music boxes
and they are applied to the teeth using a cyanoacrylate adhesive (e.g.
"super glue").

We are the sole Reuge licensed retailer and repair center within the
USA but considering that you are located in the UK, it would be much
cheaper for you to contact Reuge Switzerland directly and purchase some
Mylar dampers -- they are not expensive.  They also come in groups of
four which makes applying the dampers much easier if you are working on
a standard 3.72 or 4.50 Reuge music box.  If not, you will need to cut
and apply and each damper.

Kind regards,

Troy Duncan
https://www.singingbirdbox.com/ 
https://www.reugemusicboxusa.com/