OTL, plans were in place to send the 50th Division from Britain to the Mediterranean. However, Wavell argued that "while he would be grateful for their arrival", he more urgently needed replenishments for existing formations, particularly more technical-oriented sub-units such as signals troops, mechanics etc., and Churchill relented. The 50th, after more delays, finally arrived in theater only as late as June '41.
ITTL though, Churchill decides to scrap both options, and go for a bolder third one - send the 50th, escorted by a powerful Royal Navy surface fleet, which would rendezvous with the bulk of the Mediterranean fleet near Malta, and land it at Tripoli, effectively cutting off essentially the only remaining Italian supply hub. Without Tripoli, the Italian merchant marine would be unable to supply the 5th (and soon to be destroyed 10th) armies; without fuel, there'd be no way to bring in water to the troops; without water, people usually die of thirst within a few days.
So, they set sail sometime in late December/January, defeat the paltry Italian attempt to block the fleet (who was pretty timid during this period, so soon after the disaster that befell upon them at Taranto), land at Tripoli and take the port, ALL BEFORE THE FIRST ELEMENTS OF THE AFRIKA KORPS ARRIVE.
Without a port to supply the troops from, Hitler likely cancels the deployment of the "Sperrverband" (blocking detachment), leaving the Italians to fend for themselves.
Is this essentially game over for Mussolini in Libya?