British Campaign One: The Battle of El Alamein
The Diversionary Raid
El Alamein: October 29, 1942
As with the British campaign in the first Call of Duty, it would appear that you're going to get a taste of some commando action here in COD2. You're going to start with a raid on a fuel and ammo depot in the middle of the desert on which Rommel and his Africa Korps rely for resupplies.
Your first task here is to find and eliminate three MG positions around the level. This involves some pretty standard trench crawling, so be quick with the grenades and bank them around corners or into bunkers to ensure that no one's in your path when you want to move forward. The third MG nestn only be taken by dropping into a bunker underneath it and climbing up. You can try to clean out as much of it as possible from the trench nearby before you have to crawl up the ladder to reach it, though.
After you finish with the third hardpoint, you'll be asked to regroup with Captain Price (whom you might remember rescuing in the American campaign in the first game), and finally taking out the ammo and fuel dumps. Doing so will require you to kill a whole lot of Germans, and you should definitely do so before you head out towards the ammo and fuel dumps. Attempting to bum-rush one of these things will result in some odd auto-saving, so you'll want to lighten up the defenders before rushing into the bunkers to destroy the ammo dumps. The fuel tanks can be killed by shooting them; they'll take out any nearby Germans.
After all that's done, you have one last bunker to invade. Go in, kill everyone, and grab your documents to finish off the level.
Holding The Line
El Alamein: October 29, 1942
Now that you've gotten the Germans riled up, it's time to hold off their counterattack as they push towards a fortified town elsewhere in the desert. You've got plenty of tools to use against them, initially including emplaced machineguns and an 88mm flak cannon. For the most part, your teammates should be able to hold the line in the first couple of areas here, so feel free to hop into the 88 and use it to pound any incoming infantry before they can reach the town, or to destroy any halftracks that wander too close for their own good. There won't be any armor here - yet - so you should be able to destroy anything that comes your way with relative ease. You will have an endless supply of teammates, so that helps too!
When you shift over to the northern part of town, you'll have to leave your flak cannon behind, but you'll get an MG42 to replace it, so use it to pound the ceaseless waves of Germans that are attacking you. After they go down, you'll be asked to help target the artillery strikes that are needed to take out those pesky tanks, so head to the top of the only open building in town and use your binoculars to sight the distant enemy tanks and destroy them. You can also fire your artillery into the path of the incoming waves of enemies, if you like, but your teammates on the ground should be able to hold most of them at bay, so concentrate on the tanks. Just be mindful of your surroundings; if you spot enemies rushing your building from the streets, you can bet they'll be climbing the stairs underneath you fairly soon.
After you've taken out nine or so tanks, the mission ends, hurrah.