Here are my suggestions for holding Egypt. Lots of what to do depends on flow of battle and how good your opponent is, but here are the moves to help the British hold Egypt.
1. First turn turn in British Artillery and research Air Force. This will help in battle for Britain and Egypt, plus give your carriers better CAP.
2. Within the first six months of the game research anti-tank, tac air, and armored warfare. Inf weapons when that hits from the first chit put in it.
3. If your opponent is slower on attacking France or even fast, take the engineer that the French get and sent it to Egypt to begin digging fortifications. You should be able to get one or two fortifications done before France falls. When France falls there is also a chance that the Engineer will join the British Army, which also helps. Fortifications in France just get run over by the Luftwaffe and panzers, so not a big deal.
4. Place main defenses around El Alamein. If Axis advance that will give you the US opportunity to send tanks to help British.
5. Hit ports in North Africa, as per Hamburger Meat with French fleets the minute Italy joins the war.
If done right you will have WDF, 7th Armored Desert Rats, US Armor, and at least 2 tac air to defend Egypt with higher tech. Unless the axis have sent half or more of the Luftwaffe and 2 to three panzer corps you can hold.