The other problem with mining the Channel... well, there's more than one, but I'll just go with two. Um, three.
1) It would take an awful lot of mines to seal the Channel, a really large number to actually do the job well. Germany didn't have them ready to hand in 1940-41, as far as I know, and wouldn't have time to make them. The North Sea barrage laid in WW1 required 80 million feet of wire cable and at least 8 dedicated ships to plant 70,000 mines. The Channel is narrower, but unlike laying the North Sea barrage, people will be shooting at you while you work.
2) First you have to sweep the Channel of British mines. Which takes minesweepers. Working while being shot at and strafed, and going back over and over because the stubborn British keep using their 42-knot minelayers to put more in the water. Damned ungracious of them.
3) How do you lay the mine barrages? Remember, we're talking something approximately 50 miles wide (as a wild guesstimate average - it runs from 20 miles to over 100). The North Sea mine barrage ran 230 miles long, 18 rows across spaced 300 feet apart for about 75,000 mines. Laying 55,000 of those required 10 dedicated ships converted for the job, and took five months. Let's assume we're covering 75 miles (37.5 * 2 for the two ends), 8 mines wide (pretty thin) spaced 300 feet apart. (75*5280*8)/300 = 11,000 mines (allowing for some duds and premature exploders and assuming the Brits are sporting enough not to sweep up any).
I'm not finding information on how many mines a U-boat could lay, but let's assume 30. That's about 370 U-boat sorties, assuming they don't have anything better to do.
By bomber? From Wiki: "From April to June 1940, the Luftwaffe laid 1,000 mines in British waters." That's 10% of what we need at minimum. "The Heinkel He 115 could carry two medium or one large mine while the Heinkel He 59, Dornier Do 18, Junkers Ju 88 and Heinkel He 111 could carry more." Assume 5 (?). That's 2200 aircraft sorties... assuming they don't have anything better to do. Laying them by surface ship? Please... Maybe the Kriegsmarine could train hippos to carry them into position?
And that's assuming the Royal Navy isn't busily trying to clear paths and lay mines while the Germans try to sweep mines and lay a barrage. The RN did have a couple of specialized, extremely-fast minelayers and a large number of pre-built minesweepers. Germany had... well, bupkis is what they had. Bupkis is what they had for every important naval asset needed for SeaLion.
Oh, and:
4) The Channel is not shallow. Most German mines, from what I can tell, were large and powerful but intended to work in relatively shallow water - the explosion causes a water-hammer that breaks the ship's keel. But... over most of its width - the Channel is not shallow, so you need a mine that can be tethered at a reasonable depth.
So... no. Just not happening. Unless Germany starts prepping for SeaLion from 1933-36 there's no way they have the assets. No landing craft, no amphib doctrine, no minesweepers and layers, no naval assets in any significant quantity. I (and other sensible people) keep saying: all you have to do to test the SeaLion hypothesis is to look at Overlord. Germany fails to have ANY of the factors deemed essential for Overlord - air cover, naval assets, landing craft and a developed amphib doctrine including combat loading of supplies, friendly scouts on the ground, follow-on troops, and logistics - logistics - logistics.