Your challenge is to make sure Ottomans conquer Egypt all the way to, say, Al Alamein and hold it until the end of the war with a POD no earlier than 1 January 1910.
With a 1910 POD? That's simple and doesn't even really require too radical of a shift in events.
Italy accepts the Ottoman compromise in 1911 to gradually take administrative control of Libya (under nominal Ottoman sovereignty) without a war: it saves both of them money, face in the international community, and avoids the risks of the other Great Powers taking the opportunity to meddle in their affairs. Without the political fallout created by the lose, the Ottoman state isen't thrown into chaos by the coup against The Young Turks, which when combined with a more intact and continued reorganization/modernization of the Ottoman army, the lack of damage to its navy, and the revelation that nobody was going to intervene to defend Ottoman territorial integrity, the Balkan League dare not launch any opportunistic attacks on Imperial territory in Europe. This gives the CUP further time to cement its domestic position, continue on its modernizing vision for the state, preserves Ottoman military resources and trust in the population in its ability to protect them/fear in their ability to repress them, avoid the intensity and perception of viability of ethnic seperatism within the Empire to a certain degree, as well as deny the Serbians of vital military experiances that would give them a vital organizational and tactical advantages over their Hapsburg counterparts earlier in the war. Without either the Balkan or Italo-Turkish war, there's also significantly less evidence of the importance air power would play in modern warfare, meaning the British don't deploy airplanes in as out-of-the-way location as Egypt.
Assuming the Great War roles around as IRL (Its not like Serbian radicals are going to be LESS likely to assassinate the Archduke, since their dream of Greater Serbia is still further denied, nor Austria less likely to declare war on a weaker Serbia), and the Ottomans end up as part of the CP, they come in with an army who's morale is much higher, better stocked with equipment, supported by a more unified and functional state, and with greater faith from its minority subjects and (through the Balkans) immediate access to material and command support from Germany. This allows for a stronger push from the Levant into Egypt, where Britain: lacking air recon, don't notice the offensive quite as quickly or build up the defences of the Suez as fast. Ottoman attacks on the Suez are therefore a victory, and engineers from the Berlin-Baghdad railway project alongside military engineers from Germany work to build the rail and pipe network across the Sinai to make the military presence stick and construct defenses. With a very real presence in the area now standing behind the Sultan's call to revolt/Jihad, the local Egyptians turn (at least in subtle ways) against the British military occupation, who pressured by Senussi raids from the West and their relative isolation from support from the rest of the Empire following the closure of the Canal find their position slowly collapsing... which only triggers further and more open Egyptian resistance and panic among local Commonwealth loyalists, leading to a steady withdrawal towards Alexandria.
Italy; who's relations with the Ottomans and Austrians are (slightly) warmer in this timeline due to the successful compromise and better CP military performance in Serbia and the Middle East (LIkely including the complete destruction of the Serbian army, since there's no Albania or Salonika connection for them to escape out of) remains neutral longer, happy to allow the Libyan rebels to die against British bullets rather than undermining Italian rule in their new province. Denied a solid position to retreat to west of Alexandria by Italian neutrality with the port to supply a major military campaign, London decides trying to hold the region is a lost cause and that the troops could better be used elsewhere. A policy of "orderly evacuation" is adopted: similar to the retreat from Gallipoli if done under fire, with the army being sent to the south of France for eventual re-deployment to the British sectors in Flanders under a doctrine of taking out Germany in order to cripple its weaker partners. Al-Alamein; a non-discript hunk of rock in the desert, sees the Cresent-and-Star rise above it on a day of little import outside maybe some dusty book, maybe sometime in late 1916/early 1917