I did this fairly recently and found the key to a decisive victory is patience and mobile operations.
Each group needs to have a pionier, infantry, tank, arty - and whatever extras, a perfect blend. The air force needs to be capable of focus shooting things down one by one, no point spreading the damage. Expect some casualties of course!
Here is what I did:
*Very important: Do not move the invasion fleet.
Phase 1: Naval War and Air War
You need to hang back with the transports and send the navy in. There should be two groups of navy. Navy 1 needs to move north (where Blue is) and cut off the channel and wipe out all naval forces hanging out up there. You need to do this carefully though, a lot depends on whether you can kill them swiftly and without too much damage, because you want those naval forces bearing south.
Navy 2 should 'ring' around the transport fleet and screen them. There are some RN ships inside your pockets and naval lines ALREADY, some just inside the Fog of War. These need to be dealt with very very quickly and then the naval group needs to push west as a wall in order to destroy the navy there. This naval group is going to get hurt, because the RAF will swoop down on them. That is what you want though, when they're hitting your destroyers and ships they're NOT hitting your transports.
That's where you want the Air War - The Junkers should be nuking the RN forces with the aid of the Navy and you should be escorting them obviously. Your aim is to wipe out the navy but do serious damage to the RAF as well. All other forces, including the paratroops stay put and sit in their little tin boats.
Phase 2: The invasion
Force Blue is in the wrong area in my opinion. Force blue should be going north to take out the city up there. Force blue will probably be the first objective taken and this will provoke the AI to send some its London defences north (the train usually). Expect fierce resistance there, but nothing a small force shouldn't be able to handle. Force Blue will secure the north city and the airfield and then seige London later when the time is right. (Force Blue can take its time, no rush, I was healing a lot anyway.)
Force Red is in the right area but has the wrong objectives. it is too far west. Go a bit more East, the aim being Dover. Token infantry backed up by your air force (once the air war is done) and the mobile artillery of your navy should allow you to take the optional coastal cities after the fact. The most important part of Force red's objective should be the securing of Dover and then the elimination of the main city in the way of London (by the hills, as that is the initial defensive line in my opinion). Once those two areas are secure, you need to move very damn quickly to shift the line west and centre. Once this is done and everyone is healed, off you pop to join Force blue in a pincer against London.
Force Yellow is landing in the right area, but again, the wrong objectives. Force Yellow should shift East towards the main city objective (labelled turn 3 and 5 orange) and then SPLIT in two. One half will go West to the next objective (southern approach over the hills) and the other half will push east towards the two optional objectives on the way to London - they are decoys designed to keep the British Army in that area. If they British Army has moved to bolster London, hey all the better, you now have two free cities/airports.
Force Orange - ideally you need all 3 but it is doable with 2. Force orange is set off very carefully, you need phase 1 to succeed for this to work well. You want to land inbetween the north-west city and airfield (I think it is Bristol right?), doesn't matter if you land one side or the other. The paratroops are there to wipe out the city objectives - be warned, British Armour in that region so ensure you land in the hills and be willing to retreat to draw them into the wrong terrain. Paratroops main objective is to secure the north objective, but I ended up in a stand-off with British armour. Because of that, I sent 1 para down to tackle the city south of Bristol (northern approach) flanking it with Force Yellow, which allowed me to use Force Yellow's troops to quickly exert pressure on the southern flank of the main objective.
Ideally, the last objective to fall will be London. Absolutely nothing else matters, no side-tracking allowed, no sending your main forces off to take cities, they should only take them if they're on the way, or after the event (i.e. you have an Infantry so far back he's never going to be used in the main offensive and thus can just sit there and hold up the opposition.)
Sealion relies on super-speed, especially because you need to waste one or two turns wiping out the navy or airforce - You can ignore that and launch the invasion but you'll still be pressed for time because you're going to have to resupply and re-recruit all the losses you'll incur, transport ships get a priority target status for the RN and RAF, to such an extent that they will ignore everything just to one shot a full strength transport.
That's how I achieved a crushing victory.
