On my XJ40 the wood around the ash tray in the centre console and around the radio/AC controls has had the varnish crack and start to peel.
Some notes on my repairs in progress:
Levering off the metal 'clips' around the posts that hold the veneer panels to the ash tray assembly was really hard. Some of the clips broke.
With a very small screwdriver that has a sharp protrusion at the end due to past abuse, I've been able to chip most of the old varnish off by levering into the wood and then peeling it up from the broken edge. Often you can work it inside the separated area to expand that until it cracks off in a large chunk.
That leaves marks in the wood, but they can be reduced with 800 grit sandpaper afterwards. Sandpaper takes the varnish off too but you need it more coarse for that, and then it's easy to go too far since the wood veneer is so thin over the metal backing. I tried heating it with a hot air gun, but by the time the varnish softens the glue holding the veneer to the metal gets soft too and it comes off as well. Stripper apparantly causes the same issue.
Cabot's "Jarrah" wood stain seems to roughly match the original dark colour of the veneer where it's been covered from the light, so I'm trying that.
I'm not sure what's best for the new varnish. I've got some Cabot's Cabothane Clear Gloss polyurethane varnish which seems as good as anything I've seen suggested in old discussions online. It says "UV resistant" but also "not suitable for extreme UV exposure", so they're hedging their bets a bit. Maybe an exterior varnish would be better? Suggestions welcome (unlikely as that may be).