What would happen if the British decided to finish off Libya instead of moving into Greece, taking out Tripoli before Rommel can arrive in force? Let's say that somehow Churchill is convinced that Greece is a bad idea and doesn't opt to intervene, leaving the Greeks to handle the Italians on their own.
Does Germany not then invade Greece and leave that to the Italians? What do the Brits do with Libya? Could Tunisia/Vichy North Africa become a front or would the British leave that alone? What happens to Mussolini and his political career? If Germany does invade Greece does it fall much quick and Crete with it? What does that mean for the rest of 1941?
I had a think about this and I would suggest that better communication between Gen's Freyberg and Blamey with their respective governments (NZ and AUS) might result in those governments being disagreeable for the use of their troops in that operation.
This delays any support being sent to Greece other than advisor's, some Squadrons and equipment.
1 or both of 2 things then happen IMO
1: Germany and Bulgaria invades pretty much as per OTL - the Greeks pull back where possible and eventually evacuate forces to Crete - probably with RN Assistance.
2: The unanticipated Operation Sonnenblume (March 24th) starts and any thoughts of sending reinforcements to Greece and / or Crete are stillborn and instead those units that OTL took part in the Greek campaign move up towards Cyrenaica - this includes but is not limited to 2nd NZID, 6th AID, 7th Br Arm Div, 1st Br Arm Brigade
Of course 7th Armor is still rebuilding and would be until the Tiger Convoy arrived - so end of May before it was properly re-equipped (Tiger convoy arrives 12th May with 238 tanks) and there was a lack of transport - so I doubt that these reinforcements would arrive in time to 'stop' Rommel from reaching the Egyptian boarder and investing Tobruk
However its highly likely that Halfaya pass and other important locations in the region would still be in Allied hands and I would expect this TLs equivalent to Op Brevity to be far more successful than OTL given the greater number of uncommitted units and equipment at Wavells disposal
So I do not think that by not getting involved in Greece the British forces can simply capture the rest of Libya - but I believe that by May and certainly by the end of May the Strength of the Desert Army will be far greater and probably in possession of the Halfaya pass and other strategic positions than in OTL and therefore would be far more likely to inflict a defeat on the DAK and Italian forces in May / June and relieve Tobruk.