Italy as a neutral middleman will be of limited use to Germany, exactly because the British will apply the same policies as in WWI.
So we should look at raw materials that Italy can directly provide to Germany, and basically the only one is aluminium. I suppose they can trade that for coal, but the British in OTL did stop and hinder, without any real right to do so, Italian shipping loaded with German coal in the first half of 1940. So it's probably necessary, even if Italy remains neutral, to switch to overland trade, which can be done but puts the available Italian and German rolling stock under strain.
Italy can, of course, opt for a neutrality that is friendly to Britain, instead. In that case, the coal (and other goods) can be provided by Britain, but who would want to do that while having a common border with Germany? Plus, there is the problem mentioned in my previous post.
Possibly Italy can muddle through with a German-oriented neutrality until mid-1941. Then, once Germany has its hands full in Russia and will therefore be much less inclined to open other fronts (such as, across the Alps), can still remain neutral, but swerve towards friendliness with Britain.