I received an order from Trenietreni this morning, via DHL. Italian IVA was charged at 22%, but DHL will also be charging £47 in VAT/duty/Fees (apparently I'll get the bill sometime in the future - they didn't charge it before delivering).
I did expect this double-dipping of VAT, and Trenietreni included a receipt showing it, but I don't suppose there's any way to get back that Italian part.