I suppose a night attack withaca torpedoes can be effective in sinking or at least putting out of commission the two battleships at Taranto if, as Ssphroneth says, the necessary type of torpedoes would be available in the time period we are talking about. I say this because Taranto was such a disaster on the Italian side and that with an already declared war, while the OP seems to hint at something more sneaky, similar to Pesrl Harbor.
I think however there is also also fair chance of the attack being a fiasco because of the same torpedoes not working properly or because of adverse weather conditions and then you could have the British sqiadron at risk from the italian air force, although I am skeptical of them being seriously able to sink some capital ships at night.
This is also a time when the RM is undergoing modernization and rebuilds for several units, so the blow would be devastating. It is also clear to everyone that Italy is not on par with the British Empire in terms of power in a one on one fight, but the war following this attack would be far from easy IMO.
Sure there is the example of the shelling of Genoa in 1941, but it should be noticed that the RN did never again try such a stunt in the rest of the war, leaving strategic bombing to the air force, which would be quite difficult to do in 1936, with much less technical difference between airforces. Any naval attack to a port structure at the time must be planned very thoroughly and is a risky proposition, so even with Italy almost without capital ships I don't see the RN happily bombing and conducting amphibious operation on the he italian coasts against an intact italian army and airforce .
In short this is an hard blow to Italy, but not a knockout by far, because for that you need to seize something like.Sicily and this cetainly won't be a walk in the park for the British in 1936...
It's the political fallout however that will IMO be very damaging to the UK. Spin it as they want, give a reasonable casus belli in the Ethiopian question and what not, but this is still naked aggression, possibly treacherous even if they do something like the Japanese at Pearl harbor to ensure complete surprise. This will certainly play badly with the USA and would need a completely difficult political attitude in the UK.
I was thinking of a possibile lead-up to this being a worse crisis around the Spanish Civil War, with France and the UK openly supporting the Republic... Could this lead to an earlier ww2?
Finally,
@CalBear, with all due respect, I believe lukedalton used that word "in character" so to say, to show the level of jingoism that a British government that organises this preemptive attack would have to possess. I don't believe he would use it as an anti-italian insult, as he is Italian himself.