Had a look at my book on Alan Brooke’s diaries but couldn’t find any mention of fog in the index or in a quick scan of pages covering Dunkirk, although I might have missed something.
As a former occasional small boat sailor, I’m not sure that fog would have been a major advantage overall to the British.
My very limited experience of sea fogs (assuming Dunkirk was a sea fog) from a potential tactical viewpoint is limited to leaving a nice sunny beach and in the few minutes it took to climb up maybe 40 to 50 metres high of sand dunes a sea fog had formed and completely obscured the beach below us and for a good way out to sea. Very handy for protecting anyone under the fog from air attack, but not so handy for allowing movement of boats and ships as fog pretty much paralyses them as, depending upon the density of the fog, they either can’t move or have to move at a painfully slow pace.
I don’t know what the wave conditions were like at Dunkirk but, if I was bringing a small boat to shore through even modest waves in a thick fog when I couldn’t see more than a few metres, I wouldn’t even attempt it without the visual reference of the shore and a good view of the waves in front of and behind me. It takes very little to swamp or broach and capsize a small boat in shore waves. The closer you get to shore, the worse it gets. It would be very difficult to work out where the shore was from seeing waves a few metres away as they don’t necessarily break parallel to the shore. Admittedly, my comments are influenced by a surf beach I’m used to where you’d have to be nuts to try to bring a small boat to shore, but in gentler conditions it would be feasible and it’s not uncommon in some places for small boats to launch and retrieve from the beach without problems.
Here’s what happens when a boat handler tries to ride a wave to shore in good visibility, falls off the back of the wave, gets slowed down in the suction, probably tries to power up while being force surfed bow down by following wave, and duly broaches and capsizes. Okay, it’s a bar crossing which can be worse than beaching, but the principle is the same. https://www.youtube.com/watch?v=eaHf3QtXUws Try doing that in fog, when you can’t even see the approaching following wave you’re going to catch to come to shore.
I suppose it comes down to balancing the fog’s ability to frustrate air attacks on the evacuation and stopping observations such as artillery (although off hand I can’t recall any German artillery being in range, but I’m happy to be corrected on that) against whatever limitations it put on bringing vessels to loading points for evacuees and moving them back to larger ships or back across the Channel.
In summary, if air attacks were the major threat, then fog preventing air attacks would have been beneficial to the British if that benefit wasn’t offset more by reducing the mobility of water vessels carrying evacuees.