How is the BEF destroyed? Rundstedt and Hitler both severely underestimated the ability of the English to rescue their soldiers. No one, not even the English knew they would pull it off. Rundstedt and Hitler both wanted to conserve valuable tanks for the destruction French Army,"After all the rest of France remains to be conquered" Hitler. They both considered the BEF marooned and routed and if the British could rescue of few thousand, under Luftwaffe bombardment, more power to them. You're viewing the situation with hindsight they lacked. IMHO, Hitler and Rundstedt would make the same decision again.
Aviation fuel and the heavy fuel oil and coal that the Italian Naval vessels used are completely different substances. Germany has plenty of coal but the fuel oil the newer vessels require is hard for them to come by, to say the least.
If there is no BoB, the English will have the ability to move more aircraft than the Germans could into N. Africa right along with them. What pins them down in England? British fighter production outstrips German production at more than 2 to 1 during this period, plus the English have over 500 aircraft already stationed in Egypt and NE, with provisioned airbases and ample fuel reserves. In a pinch a Spitfire (MK's I-V)with drop tanks has about 1200 miles range, which will get it to Gibraltar on fumes from Cornwall, skirting the Iberian pen. A short skip to Malta then a hop to Alexandria, they dont even have to move them by ship.
Just as they did the UK will move South Africans, Aussies, Kiwi's, and Indians into Egypt while sailing tommy's around the Cape of Good Hope. With no Battle of Britain what keeps England from moving 3,4, or 8 divisions to Egypt? And remember most Italian aircraft are tied down in Somaliland and Abyssinia, which is under British attack.

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