Thanks for all the interest and advice.
On mature reflection, I thinks that the oily quality of this wood is probably the culprit. So I will experiment with your suggestions. Thanks again.
In response to some of your replies: -
Les - My cutting/sanding procedure? This made me think. Cutting these burls is tough, particularly the roughing. There are roots, earth, stones, etc., flying off the piece as you are cutting. You might think a burl might make a nice candle-stick, but it ends up as an ash-tray. They are hard, so re-sharpening tools is essential. The grain is all over the place. Not sure I have a procedure. As to sanding, I leave the piece for a few days to let any oil come out, then wipe dry, apply sanding sealer and sand up to 320. Then I have tried Yorkshire Grit, which gives a nice finish, but if the piece is full of cracks and crevices (which these burls are), then its difficult to get the YG out of the cracks & crevices. I have also tried Chestnut Woodwax over this. Again, its difficult to clean stuff out of the cracks. This often gives a patchy finish, so I have reverted to multiple coats of sanding sealer, which gives a duller finish, buts it is not patchy.
dr4g0nfly - Thanks for the tip on acetone. Didn't know it was useful for CA glue.
Lazarus - Not familiar with Truoil, but as it contains linseed oil, I think I might be compounding my problems with oil.