The Australian Official History has an assessment of General Wavell and the events towards the end of his tenure. For Admiral Cunningham, he had a glowing opinion of General Wavell. They had served together during the hardest of times in 1941. The battle for Crete was perhaps the most trying time. Admiral Cunningham considered General Wavell to be a great general, "if not the greatest".
General Wavell got credit for the brilliant campaign against the Italians conducted by General Richard O'Connor. General Wavell also took responsibility for the loss of Cyrenaica to Rommel. They blamed the loss on an incorrect estimate of the Axis strenght. Really, however, Rommel was an expert in infiltration tactics and the modern embodiment of that tactical idea in Blitzkrieg. With Rommel's arrival, the British commanders on the spot were not prepared to combat him, regardless of his force strength. Richard O'Connor had serious health issues, but he was put in the bag when he appeared as an advisor.
General Wavell backed Churchill's Greek adventure. That is not something to brag about. The campaign was politically motivated and was doomed to failure before the campaign started. General Wavell had to lie to the Australian Prime Minister and senior army officer to get them to agree to participate. The operation was obviously doomed to fail to anyone who understood the issues. The loss of Crete was a foreseeable consequence of the loss of Greece.
Wavell was reluctant to participate in the campaigns in Iraq and Syria. He was pressed to do so by Churchill. Resisting the Iraqi rebellion made sense and was successful, ultimately. As for Syria, there was not a pressing need to intervene when the attack came. Churchill misunderstood the Vichy French position and he was blinded by his hatred of them. There were really not the forces needed to invade, but they invaded anyway because that was what Churchill needed, politically. We suspect that he was looking for a quick victory over someone that he could brag about. Both the Germans and French were reluctant to do anything in Syria to prompt the British to invade. The French had briefly cooperated with the German attempt to aid the insurgent Iraqis, but quickly backed off. The Germans were particularly concerned about the possibility that the British would be provoked into invading. Because there was a political need, the Australians went into Syria with inadequate strength. They ultimately succeeded due to the quality of the men and their leadership, but they took heavy casualties in the process that might have been avoided. In any case, General Wavell's usefulness to Churchill had come to an end and he was sacked. This is based on the account in Vol.II of the Australian Official History and our editorial comments.