I have left the UK in the past in CAVOK Got to the channel and crossed with extensive fog over the channel!
One occasion the fog was so thin there was almost a Salvidor Dali picture of ships funnels carving trails through the fog
I was in a twin.
Having said that in a single in that situation I would have had an out. Fog is likely to equal calm glass like sea.
Thin fog and maybe a radar altimeter set at 30 feet! Flair and chances are you may do a half reasonable landing on the sea surface
Pace