Based on the "Second World War" channel, the British could have hold Crete, but due to "stupidity", they lost the island to the Germans. But what if they have hold the island, what use could it be made for the British (and Americans later) for the Army/Navy/Air Force?
You have to consider or think of Crete as being effectively 3 large Islands - connected by pretty poor land bridges as far as the geography goes
While on paper the 'British' and Greeks have far more troops etc than the Germans they have a few problems
The Greek forces a mixed bag of about 10000 men had just 52 odd LMGs between them - the Ammunition they used was one that the British did not and while they had just about enough rifles (and a mix of types and calibre at that) for the fighting units many of the Infantry had less than 30 rounds a rifle and some had none which seriously limited their effectiveness.
The NZ division - the principle fighting unit - while it had suffered some losses in Greece it had retained its cohesion but the biggest issue was the loss of much of its MT and heavy equipment including most of its artillery when it was evacuated.
So its and the various Infantry Brigades and composite 'infantry' units ability to move around (remember consider the place to be 3 islands) and respond to the invasion was severely constrained.
Lack of Radio and reliance of wire communication and runners resulted in the confusion that was the Kiwis abandoning the defence of Maleme Airfield and allowing the FJs to recover from their fucked up failed 4 LZ plan (and failed seaborne landings) and concentrate the follow on waves at a single point (Maleme).
The failure to immediately counter attack by the 2nd NZ is again down to poor comms and inexperienced staff officers (who believed that a sea landing must naturally follow and had deployed accordingly - to be fair they would have been aware of the navys attempts at intercepting them) as well as the armys inability to recognise the importance of the Airfield to the campaign allowing the Germans to establish an Airhead.
So how is all of this addressed?
Well I have a POD for that.
The Australian and New Zealand Commanders drag their feet over the Greek deployment and rather than simply accepting the command at face value about their respective governments being happy about this adventure instead demur and seek political guidance.
This kicks off a bit of a crisis between the various heads of government and by the time permission is given its too late and the Germans have already stolen a march
Realising that it is too late to deploy the expeditionary force to Greece - combat loaded forces (Principally the New Zealand Division) are deployed directly to Crete - while the ships intending to deploy the Commonwealth forces are instead used to evacuate the Greek forces from the mainland.
Many of the Greek combat units are landed on Crete and it is decided to rearm them with weapons, equipment, AFVs and some artillery taken from the Italian's during Compass until such a time as Commonwealth equipment can be used to rearm them.
In time it is hoped that they will be able to take over the main responsibility for the defence of the islands
The 2nd NZ Division as well as the other principle Commonwealth forces ITTL has all of its ToOE including its full allocation of MT and Artillery and other equipment making it much more mobile than OTL and having better communications.
Far more units of the Greek army have been evacuated and these units lack of equipment is rectified in some part with Italian equipment, ammunition and supplies - everything from Carcano rifles to Brixa mortars and Brida Machine guns as well as several dozen L3/33 Tankettes and enough artillery to form several battery worth of artillery
The additional sealift allows for more of the 'useless mouths' to be evacuated than OTL.
The upshot being that the Greek forces are able to make a far greater showing and the Commonwealth formations have far greater mobility and cohesion and are able to more readily react by concentrating greater forces at any LZ.
The 4 principle LZ are effectively snuffed out but unlike OTL there is no mistake at Maleme and after several days of trying to force through seaborne it becomes clear that the first waves have been destroyed and the German commanders reluctantly call it off.
Losses to the FJ in terms of dead and wounded are lower than OTL but POWs are much higher with the first and in some cases 2nd wave formations of the Principle fighting formations of the 7th Flieger Division and
Luftlande-Sturm-Regiment 1 being totally wiped out and in many cases those units being reduced to cadre.
The Luftwaffe Falshirmjeager units are effectively disbanded following the Crete Disaster with the manpower used to form the core of several Luftwaffe field Divisions
Years later it is suggested that Admiral Canaris head of Abwehr had deliberately mislead the German high command by claiming that there was in addition to the lightly armed and 'disorganised' Greek troops only 5000 mostly Lines Of Communication (RAF etc) commonwealth troops on the Island which explains the somewhat foolhardy very optimistic 4 wildly dispersed Landing zones rather than one concentrated one which 'might' have had some chance of success.
ITTL with no desperate attempts to relieve and then evacuate the Allied forces the RN suffers fewer losses.