Thank you for all of the ideas and suggestions, and the different types of glue to consider.
Acetone. I have a bottle of that in the garage, but would not have considered using it to clean the wood. I shall try some on a piece of spare, as well as thinners, to see which seems most effective.
Spreading metal ring into the wood. I had not considered that, I confess. I am not quite sure how I would manage it without hammering, but I imagine that I could fabricate something with a tapers and a bolt to draw them together to expand the metal.
Dalboy: I like your bowl, which looks rather 1930s. Is the pattern around the top the pattern from an old bowls ball or something that you created?
Vic: thank you for the link, which I shall read.
I bought two old lignum vitae bowls balls yesterday, so when they arrive, I shall be able to make a start.
Watch this space…… but not for a while.
James.