They have the air power and the Regia Marina wasn't that outdated. As I said, Paratroopers a la IRL Crete. If the initial assault does fail, there's a good chance the Italians and Germans will sieze the Suez and ...
The Italians/Germans taking North-Africa up to Suez is logistically close to impossible.
IIRC they can at most supply 5 divisions from the ports in N-Africa untill they controll Alexandria.
If you consider the Axis will also have to defend all those little ports on the coast, like Tobruk and everything valuable like Tripoli, they are not going to have much left to go onto any offense.
To make matters worse their supplylines will be extremely long by the time they come anywhere near Alexandria. Much of their supplies will have travelled 1000+ km since arriving in N-Africa by the time it reaches their troops.
Because of Dunkirk there's also the possibility there'll be no Allied intervention in Greece as another poster mentioned. If the British decide to play it safe and keep their forces in N-Africa, one of the consequences of a failed Dunkirk could be the complete destruction of all Italian forces in Libya by feb '41 or so, which would be too soon for any German intervention in N-Africa to have any lasting effect.
you'd likely have Spain join the Axis for Gilbraltar. This would seal off the Mediterranian effectively.
Having Spain in the Axis is also not going to happen if only the BEF is lost. Hitler wanted to keep Vichy France a friend and one of the conditions of Spain joining the Axis were large parts of the (then) Vichy French colonies, apart from such large amounts of food and arms Germany wouldn't be able to supply them.
IRL several tens of thousands of Spanish died during WWII of starvation IIRC. That was while having enormous imports from especially the US. How many Spanish are going to die without these?
So essentially there's no chance of Spain joining the Allies.
Besides, Spain was completely ruined thanks to the Civil War. No leader, short of an insane one and Franco is definitely not insane, is going to jump into a world war.