England's motivation was always to secure that region. The work was done during centuries. Softening the folks living along that route. Softening for English influence and intervention. This is what the "Soft Underbelly" really means (Szálasi does not say this outright this is my conclusion - he says it is soft because soft folks live there). In military sense, conquering Europe from the South is a nightmare, getting a grip on the nations by England however, is relatively easy.
So whatever happens, it's a natural thing that England wants to be in control here. When Italy entered the war they tried to take Tripoli by storm. The Germans had to intervene, take over the control and push the Brits back. They even managed to pinch that artery, and prevent sailing through the Mediterranean.
Then with Japan's sudden expansion, a new front opened up for the Brits in the East. Burma was taken from them, and the Japs stood at the gates of India, threatening the Eastern base of the British Empire. The importance of the European Southern Theater rose. Now it meant a channel not just for the resources moving to the Isles, but troops and war material back to East. But there was another reason: among these circumstances (it's 1942 summer when the Germans were at the Soviet Crisis line, expanded toward the Caucasus, the Japanese also at their height of expansion) a possible joint Tripartite Pact action could be expected if something drastic not happens. So the Southern Theater could turn into a springboard for the Axis into the Middle East, toward Persian Gulf. However Szálasi saw quite a few conditions to this happening (and in late 1943 these were even farther than in '42 summer), I'll list them later, I want to continue with England.