How so? If the barges were properly protected, they could've done the job.
All the Germans needed was to get control of the airspace over the channel and S. England, gather forces for an invasion, launch paratroopers and capture airfields in S. England and mine the crap out of the channel. If the Luftwaffe played their cards right, they could've made the RAF collapse and open the UK up for a German victory.
Sorry to have taken so long with this, here's the main problem areas:
RAF Withdrawing North
Royal Air Force doesn't plan on collapsing and getting every single fighter destroyed. The fighter wings were to be transferred to northern bases in Scotland to rregroup and rebuild out of the Luftwaffe's range. Come D-Day, the British can bring them back and contest the air somewhat.
Luftwaffe Doesn't Have The Right Planes and Tactics for Sinking Ships
The Luftwaffe can't actually keep the RN from intervening. They don't have any single-engine torpedo bombers at the time, no trained naval bomber forces, and had in fact done a pretty pretty embarrassing job of sinking easy targets up to that point. At Dunkirk, against sitting duck naval vessels loading troops in an enclosed space, they only managed to sink six out of forty-two RN destroyers. The tactics and technology that helped them score high kill rates later on around Malta and Crete simply have not been developed yet. And even in Crete, with the Luftwaffe in absolute control of the skies, they still couldn't protect transports by sea, and the paratroopers had to be reinforced from the air alone.
RN Home Fleet is Just Too Big and The Luftwaffe Has Too Much To Do
There are also just too many RN ships to hit. There's a carrier, five or six capital ships, and something like a hundred cruisers and destroyers based in the Home Fleet. They'll take some harsh punishment to be sure but even in the most ideal conditions, there's no way the Luftwaffe will be able to sink the majority of that fleet before it gets in the way. The Luftwaffe also has to divide its forces between other key missions as well, including close air support for the landings, maintaining air superiority, hitting the rail network, and raiding civilian targets to get the refugees onto the roads.
Negligible German Surface Fleet
Hardly any major German naval units even available. Bismarck's not done, Scharnhorst and Gneisenau are out of action, half the destroyer fleet was lost in the Norway campaign. If I remember correctly, the only major surface units that were to actually accompany the barges were ten destroyers and one light cruiser. The only major units available were Admiral Hipper and Admiral Scheer, and it was planned to send them out on sorties as decoy targets.
U-Boats Aren't Cut Out for Channel Battle
The U-boats will be massacred if its a brawl in the Channel. WWII submarines were small boats and these are 1940 ones with torpedo issues. Submarines are simply not meant to duke it out in enclosed spaces of water with surface ships. Realistically the U-boats get one chance to ambush the leading elements of the Home Fleet (which were probably be the destroyer and light cruiser escorts, not the battleships) and then they'll be slaughtered by the rest of the fleet. The British cruiser and destroyer force outnumbers the U-boats here at least 2 to 1, and that's not even counting the thousands of various small patrol craft as well.
Germans Outnumbered in Small Craft, Short on Minelayers and Minesweepers
Speaking of small craft, the British also outnumber the Germans here several times to one. The Germans are relying on E-boats and other little ones to actually do most of the escort work. The British have thousands of small craft which can at minimum shoot up the barges. The Germans don't have enough minelaying vessels to completely block the Channel at all before the Home Fleet arrives. The Germans are also short of minesweepers themselves - the British laid a lot of mines as well.
The Germans Can Only Get a Limited Army Across
The Germans can't get enough men across. Their optimistic estimate was just barely being able to bring across and sustain ten divisions if all things went right. This is ten divisions short on artillery and tanks, by the way, since wasn't enough capacity to get many across the Channel and those that did would have had to go by very haphazard means (either loaded up in slow fat freighters or floated across singly on barges). That's still a very strong force early on when the British army is at its weakest, but victory would depend utterly on forcing the British to capitulate with a quick capture of London. Given what we know about Churchill and the British, the fall of London would not end the campaign at all. The British wer mobilizing hundreds of thousands and would have soon badly outnumbered the Germans. The Germans also lose their capacity to reinforce and sustain the campaign as more and more barges get sunk, and worse, also lose their capacity to evacuate with every barge that goes down.
And They Can't Supply It Effectively
Supply, supply, supply. Just like the game. Germany had very little of a freighter fleet for a nation of their industrial standing, and what big freighters they did have were being prioritized for decoy missions to draw off the Royal Navy and transporting heavy equipment. Actually supplying the landed divisions would fall mainly on the barges...it's plausible for most of the barges to make a first trip or two across the Channel if the weather is good and the RN is kept away, but just imagine the attrition they'll have suffered after a week or two. And the Germans can pick a good day to launch the invasion, but those stretches of good weather can only be counted upon for a few days, maybe a week at most....the moment it starts to storm or even gale in the Channel, 90% of the German supply fleet would be unable to cross the Channel.
Germans Had No Practical Experience with Amphibious Ops
The Germans had not had practical experience with amphibious warfare yet. Remember how the Dieppe Raid worked out? That and the island hopping in the Pacific was where the Allies learned the do's and don'ts of invading enemy territory by sea. The Germans have had none of this and this will be where they make their mistakes - just about everybody bungled their first amphibous operations against defended targets - the disastrous British/Canadian Dieppe Raid, the Japanese embarrassment in Wake Island, the American bloodbath on Tarawa (we won and the Japanese lost more, but over 1600 men were killed for a few pebbles).
Haphazard Planning and Terrible Command Structure
German planning is extremely rushed and the branches of their military are abysmal at coordinating with one another. All three branches were throwing together their own individual plans and Hitler appointed no single joint commander. Germany had not really made contingency plans for invading the UK and the final form of the Sea Lion was essentially something slapped together at the last minute. Compare that with Operation Overlord, in which over two years were spent planning and assembling the resources for it.
Now, there are ways Germany could have addressed some of these problems, but it would have taken a combination of almost all of them together for it to work, something not likely from an alternate history point of view (but plausible in hindsight). In history as it happened, it's a virtual certainty the operation would have failed if launched, even if the Luftwaffe had won the air campaign. I personally think that maybe if the Germans panzers had captured the whole BEF at Dunkirk, if the Norway invasion hadn't trashed the Kriegsmarine so badly, and if they'd won the air battle (and maybe if Vichy France had declared war after Mers El-Kabir and forced the British to reinforce the Mediterranean), then maybe there could have been a chance of success - but still an enormous and unlikely gamble.
Of course, in a Hearts of Iron scenario, where the player's in charge and preparing Germany for war with UK since 1936, it's entirely possible not only to avoid the historical mistakes and do the things Germany theoretically could have done, but also to stack the odds in your favor the way real life Germany never could - getting the battleships into water in 1940, build a merchant marine bigger than the UK, call in Japan in 1940 (and a Japan that had conquered China no less), etc.