No Greek intervention by Britain: complete victory in 1941 in Libya?

  This is something I've toyed with a lot.  Probably not with that POD as the last stages of the Cyrenaica campaign involved the thrust across the desert to cut off the Italian forces retreating from Benghazi.  Which because of the rugged terrain really wore down the forces involved, especially their motorised and tracked stuff.  As such even if Churchill had been willing, or General Metaxas hadn't died suddenly it might have been difficult to reach Tripoli with the forces that would have been available.  Especially not before Germany intervened.  The logistical problems would have been huge.

  A better option which might have worked would have been if Churchill hadn't decided to invade Italian E Africa.  The 1st stage of Compass had seen the WDF [Western Desert Force] destroy the Italian forces which had crossed the border and advancing to capture Sollum, Halfaya and Fort Capuzzo.  It consisted largely of 7th Armoured Div and 4th Indian Div.  However at this point as part of the plan to invade E Africa the 4th Indian was withdrawn to take part in that operation.  It was replaced by the 6th Australian Div but it took some time to bring that unit to the front and get it acclimatised to the conditions.  As such there was a decay of about 3 weeks before the attack resumed in early Jan 41.

  A small break to regroup might have been best but if the 4th Indian had been kept in the region, with the 6th Australian as a reinforcement the campaign in Cyrenaica could have been pushed faster, which would have given the Italians less time to regroup and build defences.  This might have avoided the ruinous advance through the desert to cut off the retreating Italian 10th Army.  If nothing else the 6th Aus would have been available to help with the problem of handling the large number of prisoners and take over at times while the 4th Ind took a break to regroup.

  In turn if this was done earlier Wavell might have been able to push for an advance towards Tripoli ASAP and this would be under way before Metaxas's death removed Greek opposition to British forces landing there.    Such a campaign into Tripolitania might have succeeded before Italian morale recovered and Italian and German reinforcements arrived.  The Italians historically by the end of the Cyrenaica  stage were down to 4 divs and a few escapees from 10th Army.  So despite the huge logistical problems it might have been possible to get to Tripoli before substantial reinforcements arrived, especially without air, naval and ground forces diverted to E Africa and Greece.  Its even possible that, desiring the earliest possible campaign against Russia but fearing an Italian collapse on his southern flank Hitler decides to intervene in the Balkans as OTL but give up Libya as lost.  Or is persuaded by his generals that Britain can't push that far in time.

  See Operation_Compass for more details, especially the section on the WDF and the "subsequent operations" section which notes the denuded status of the units left in Cyrenaica after forces were sent to Greece.