Returning to the origin of this topic, let's assume that the opening post was not about Gibraltar, which we can all agree was under British possession and Franco was completely unable to give it to any other country, but any other Spanish base in the Atlantic.
As already mentioned, this action by Franco would have caused a strong British opposition, both towards Spain (under British control for its imports, especially food) and Germany. We should recall the "Easter Agreement" signed by Italy and UK on 16 April 1938; one of the conditions most firmly put forward by UK was that Italy retreated its armed forces from the Balearics as soon as possible. It was a conditio sine qua non for the negotiations and it can be regarded as a good example of the stance that UK would have kept if Germany had managed to get a naval base on the Spanish Atlantic coast.
I see that the chance of an Italian Navy's activity in the Atlantic has been raised too. This idea surfaced more than once during the Second World War, always under the assumptions that Spain had sided with the Axis (or even forced to do so after a German occupation, ostensibly to prevent the menace of an Allied landing) and Gibraltar had been conquered or at least besieged (losing its offensive capacity, i.e. its ships and aircrafts).
As far as I know, no actual planning was ever made, given that it was a relatively remote hypothesis, but it would have to face some serious problems, anyway:
1) The British, through the Suez Channel, could have reinforced the Mediterranean Fleet in Alexandria. This force ceased to be a menace since the sinking of the Barham in Nov. 1941 and the damages inflicted on the Valiant and Queen Elizabeth in Dec. 1941, so the problem of a new battle force in Alexandria, especially after the sinking of Repulse and Prince of Wales, was regarded as a minor one, but until the beginning of 1942 it could not be ruled out.
2) The Italian Navy was always hampered by the very short range of its destroyers, which were the most obsolete component of the fleet. This map, by Vincent P. O'Hara, provides a clear indication of the maximum range of the Italian fleet (from its main bases of Spezia and Taranto and the secondary bases of Naples and Messina), due to the limitations of the destroyers.
In the Atlantic, this shortcoming, given also the lack of fleet tankers, would have been dramatic. Precisely for this reason, the Breakthrough Fleet, planned before the war by adm. Cavagnari but never really implemented due to lack of money and of the Diesel engines planned for the oceanic cruisers, was based upon the "espolatori" (scouts) of the "Capitani Romani" class. The first ones of these beautiful, very advanced and successful ships were the only ones which managed to enter in service and fight in WW2, reclassified as "light cruisers". In the original plan, they should have operated as very large fleet destroyers for the oceanic operations, thus overcoming the limits of the usual destroyers.
3) The lack of fuel was of course another serious limitation, which would have been overcome only if the escort to North African convoys could have been made by minor vessels, such as corvettes or motor torpedo boats.
Despite these problems, for a short while the chance of an Italian Atlantic fleet was taken into account by Mussolini and the High Command of the Italian Navy. It happened at the beginning of 1943, when Mussolini hoped that the defeat in Stalingrad would have made Hitler sign an armistice with USSR, or at least would have made him order a strictly defensive stance on the Russian Front, therefore freeing enough divisions for the (more or less friendly) occupation of Spain and the defeat of the Allies in Algeria and Morocco, while the African front would have been stabilized along the Mareth Line on the border between Tunisia and Libya. This would have meant that the Western Mediterranean would have been turned into an Italian-controlled basin, leaving the escort of convoys to unexpensive and fuel-saving small units.
In January 19443, this one was the extremely optimistic scenario in which Supermarina developed the plan for the Navy for the year 1944. By the end of that year, the Italian Navy planned the availability of a battle force of 9 battleships and 4 aircraft carriers:
- 3 "Littorio" class battleships;
- 2 "Duilio" class battleships;
- 2 "Cavour" class battleships (both Cavour and Cesare would have been updated with new AA artillery, etc.);
- 2 "Dunkerque" class battleships, repaired in Toulon and put into Italian service;
- 1 fleet aircraft carrier (Aquila);
- 1 escort aircraft carrier (Sparviero);
- 2 light aircraft carriers (former heavy cruisers Bolzano and Foch, repaired and turned into aircraft-launchers).
Hitler's refusal to reach an agreement with USSR and the limited success of the battle of Kasserine Pass turned this scenario into the realm of unfeasibility within a few weeks.
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