It looks like it is just a square of cloth 'stuck' onto the wood base.
But life is never that simple! Anyobe ever done this please?
Does the green cloth perchance come with a peel-off stickey back? Probably
not.
Glue?

Any advice on how to proceed much appreciated.

Dee

My father was a cabinet maker and I am sure he used to stick it down with
a glue which he melted in a pot. Try asking around furniture restorers.

Dave