Flying over fog
I did Plymouth to Leeds-Bradford a couple of months ago at night crossing over an almost completely foggy UK. I didn't see any ground lighting all the way from departure from Plymouth (which was clear) until 20 miles South of LBA.
LBA was CAVOK as it is up on the top of a hill.
Humberside (my origninal destination) was fogged out as was practically everywhere else.
Pace and IO540 are right about fuel, fill right up.
Prior to the flight get the TAFs abd METARs and know what the extent of the fog is likely to be. It is worth printing these out so you can refer to this info in flight.
En-route use your radio to listen to the ATIS of each airfield you pass, tune in to VOLMET and don't be afraid to ask for weather from ATC en-route, or if they're too busy call London info on box 2 and request it from them (just like the airlines do).
SB