Unfortunately, as others have suggested, he is caught. If he didn't own the other unoccupied property, the relief would have applied to the inheritance of the second property. One of the main conditions is that the recipient does not have an interest in another dwelling. The relief couldn't have applied to the first inheritance either unless your uncle was living there. How much tax is involved?
When someone inherits a property that they're living in, the "valuation date" is the date of death. The only possible solution I can think of is the uncle disclaiming the inheritance, but that would only work if the "next" next of kin was living in the property. I think that the tax is unavoidable here unfortunately.