Quite simply, i build ARM. Only ARM. I leave the worthless defensive doctrine as the game starts, and i go for mobility. the UK gets Someone whose last name is Hull, and he is at least as good as the german blitzkrieg theorists. For a small 5% dissent hit, and assuming no random cabinet switches, he can stay and give you a great tech team and good bonuses as an armored spearhead commander. Keep the infantry the UK starts with if you want, though i usually disband it and go with garrisons with Arty/AA, and a serial run of 6X armor divs, that grows to 9 or stays at 6 since about 1937/1938 (since you need the armored division doctrine that mobility gives you right after you research Delay doctrine from the mobility land doctrine). The UK has to play it smart; Your main focus is to make sure that the germans do a few things:
1) Make sure they pay for the invasion of France.
2) Make sure they take a long time to beat the soviets
Why? the first one is to slow down their wanton army building. by may 1940 the germans will have a large superiority over the french, both in numbers and in doctrine (its the mod, you see), so you must make sure that you delay the krauts from winning too fast. stay close to the northern shore and focus your entire airforce to defending the pass, and you can buy the french a month or two of respite to allow them to weaken the german MP a little. To put it in contrast, a german army that attacks france without UK support can take it in a few weeks, exploit the full IC of the country (i play with full IC occupation option, so german IC reaches monstrous levels later on), and their army will have grown a lot since start to finish. a german army blunted, at least on the start, by a somewhat agressive defender UK force, can heavily slow down the german army building program. Also, the longer you hold them back, the bigger the chance the germans will wait until the next year to attack the soviets, when they will at least have somewhat of a fighting chance. Dont worry too much about africa; 12 arm divs can destroy the entire african theatre in two months, tops. remember to send a force to conquer ethiopia though.
The second one is a lot trickier, but it fits in with the UK strategy. The trick is to keep germany busy right after barbarossa starts so that they will have a hard time vs the soviets, who will get weakened also, but not to weaken them so much that the soviets steamroll them right back. It's a very careful balance.
For this, as soon as the germans begin to overwhelm your french allies in france, start to take your forces back (disband any now-UK-previously-belgian/dutch infantry, if they cant get out), and start going to africa. I also should have told you to set up a lot of AA back in the UK, especially the ports, to dissuade any bombing attacks by the germans. And even if they do, they will lose obscenely large amounts of bombers on the job, unsustainable for them. send ALL your fighters to africa, and base some at malta and at recently conquered african provinces, to secure your airspace around Italy, which will be your next hurdle. ready your forces, and as soon as germany DOW's the soviets, go invade Italy.
Now, i probably should tell you why not france. Simply, redeployment for the AI is ridiculously fast, and the germans keep good divs defending their shores. As soon as a landing is attempted, expect half the german army in occupied france to come stop you, not to mention bomb your fleet. the italian AI will not do a good job defending their shores, especially after you destroyed their whole army back in africa. Once landed, begin to push north immediately, worry about the surrounded italians later. The germans will send a large force to stop you, but that is the point, to keep the germans occupied on a second front while your soviet allies get some breathing room. Germany cannot sustain both pushes for long, and they will lose lots of MP not just to you, but to building constant divs, not to mention that their repair costs will soar through the roof if they launch a lot of suicidal bombing runs on your forces on the UK (which is why i get arty/aa garrisons, remember? well dug in AA garrisons getting attacked by german bombers will lose one or two men per raid, while the germans lose 30 or more bombers).
Now comes another, not so tricky part. Depending on how far the germans are in russia, keep pushing onto northern italy. Remember, if it gets overwhelming, you can always retreat safely, but try to push on regardless of losses to you. You see, armor divs do not utilize as much MP as infantry or motorized divs, and take less MP to recover, but a lot of IC to fix. That's why armor is good for countries with high IC/low MP, like the UK, even though they dont really get that much. Eventually you might get the event that the italian regime collapses, and no big deal there. in fact, this will make the germans send more divs to slow you down, so it's good. Be agressive despite the losses. Repeatedly attack a german province from 3 sides, even if the first time you lose. The germans will not gain reinforcements faster than you, and if you get the 20% org bonus minister (which you should, always), plus Churchill, you get a lot of fast recovery. And also, the germans have to devote IC to other tasks, and cannot keep up their fixing schedule. With the italian captured IC, you should have somewhat enough to replenish your losses. Attack and attack some more. keep driving north.
Finally, it's all about how much balance you have. If you see the germans have stopped expanding onto soviet russia or are losing terrain to the soviets (fully viewable with FOW, but i guess that if you want to check it real fast you could do the toggle_fow cheat. no peeking on Germany!), then stop advancing and launch a few small spoiler attacks to weaken their MP. If the germans are going wild bill on russia, then push faster. Needless to say, keep reinforcing italy.
Now comes a nicely mischievous thing you can do, depending on how much land you want after the war. If the germans are out of MP, and have done extended mobilization, let them BP the soviets, so that you can conquer more off of them later. You should avoid going into a general mobilization as long as humanly possible. Because the UK is an island nation, the manpower ministers, even the ones that give foreign manpower bonuses, are quite worthless. Besides, you have your foot infantry that you can disband for MP.
