A winter high pressure holds haze and as the sun descends through this layer, it can completely take away your horizon.
Not quite the same as a cross channel flight. A haze can usually be seen in METARs and TAFs and although it is hard to predict accurately how hazy it will really be, the fact that there will be haze can be easily forecasted and anticipated.
However, over the channel you can be in perfect CAVOK conditions and still be in IMC, for all practical purposes. Simply because CAVOK means a flight visibility of more than 9999, but at FL45 (a typical channel crossing altitude, to remain clear of controlled airspace above), the horizon is more than 10 km away. This means that the sea blends into the sky and you see no horizon whatsoever around you. The solution is to fly lower, or look below you for clues about your attitude. Or switch to instruments/AP.
This is something that has to be seen and understood, and is one of the reasons that I can imagine a cross-channel checkout would be required for novice pilots.
Although I have to say I've flown cross-channel a number of times now, never had a checkout, and never had a problem either.
The only difference, apart from the academic paperwork, between a flight to the continient and a domestic flight is the call at the FIR boundary, and the paperwork could be filled in for a ficticious flight at no real cost.
The call at the FIR boundary is completely standard. It's usually a handover from one controller to the next, occasionally a freecall. If you've flown within Europe, it's exactly the same as crossing a FIR boundary over land. The flight plan is also equal for a continental flight that crosses a FIR boundary. The only real difference is the GAR form, and that form has detailed instructions on the back. And even if you can't understand these instructions, you can simply fly from one customs field to another, just like we did on the continent before Schengen.