Had the Italians covered a major invasion force with battleships, supported in turn by the Luftwaffe operating from Sicily, I don't know that the RN could have defeated such a force.
The RN would've routed the Italians in a night action, just as the Italians feared given their lack of ship-borne radar and deficient training in night fighting. The Luftwaffe would have a nice view of all the sinking troop transports when they took off in the morning.
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