Out damn spot
Al is very funny. I always luv a good duck tape joke. But seriously, it looks like an emergence of moisture from under the enamel surface. It’s quite possible that by throwing those dry-packs in, you inadvertently triggered movement of moisture in the wood. Was that the gravity downside, the way the set was stored?
Quite possible it was facing down? The moisture absorber packs weren't next to this particular piece, and I just had a couple of small packs per shelf in the coffer.
I've had a crack at cleaning it with just soap and water. It seems to have taken the polish off, and once dried, the spots are still visible, but much less so. I'm just using a soft cloth - I didn't want to abrade the piece. I imagine if it was 'emergent moisture' then allowing the piece to dry with the wax/polish removed should solve the problem? I'll give it another crack and a bit more elbow grease and see how it looks once it's dried again. Thanks for the advice.

Can't imagine what "emergent moisture" is, water will be distributed through the wood, not sitting in a corner waiting to escape. The life expectancy of the silica gel sachets exposed to air is limited and if the house has mould due to the weather there, the set will get damp to some degree too and the spots could be mould. The pieces are likely to be varnished or lacquered, possibly with a wax coating applied over the top. Washing adds more water and will remove the wax, possibly adding some cloudiness to the finish which could hide the spots. Adding Renaissance wax will add an additional layer of polythene, but if the problem is mould under the finish you need to get the piece quite dry before adding more finish.
The western dessert lives and breathes in 45 degrees. One of my favorites!
The issue is most likely due to gravity downside, rather than mould, given the climate in Aussie-ville. Your emergent moisture from gravity downside is likely the culprit.
Try resting the piece in a bowl of salt.
Although I live in the Midwest, I can say we have some very nice desserts.
There is on place that makes an excellent Blueberry Lemon bar. And another makes an exceptional Blackberry Cobbler. Now, we're talking desserts!
I imagine if one lived in the desert they would probably have some kind of cactus for dessert!

... The issue is most likely due to gravity downside, rather than mould, given the climate in Aussie-ville. ...
The OP said they have mould spotting in the house, meaning that the house is damp. The "climate in Aussie-ville" is about as meaningful as talking about "the climate in the US", the countries are similar sizes.
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Hi Guys,
I've just noticed a pair of spots on my white Morphy King and was looking for advice on how to clean/fix it.
I have no idea what caused them, I keep this set stored in a wooden HOS coffer with some anti moisture packs thrown in. None of the other pieces have spots, it's been ages since I last looked at them but it's winter here and we have had mold spotting in the house so mold is my best guess?
Should I send this to a restorer? Can anybody recommend one in Australia?