Finally, LCY:

at 12:50 today: variable wind direction at 3 knots, 5 Km vis in mist, some scattered cloud at 400 ft AGL, some further scattered clouds at 600 ft AGL, and a cloud ceiling at 900 ft AGL. Temp of 2 C with a dew point of 1 C. Pressure of 1029 hPa.

(a comment about the previous drizzle and rain reports that Swanhunter was mentioning were likely incorrect...I expect this is due to the automatic station using a rain gauge for precipitation measurements and it takes a while for the snow to melt which then would be reported incorrectly later and appear to be of a moderate intensity when it finally melts...so maybe this was the issue earlier on today).

METAR EGLC 051250Z VRB03KT 5000 BR SCT004 SCT006 BKN009 02/01 Q1029

Forecast (I believe from a military base nearby within 30 Km):

TAF EGLC 051108Z 0512/0521 VRB05KT 4000 BR SCT004 BKN008
TEMPO 0512/0516 6000 NSW BKN015
TEMPO 0516/0518 BKN004
BECMG 0518/0521 BKN004

issued at 11:00 today covering a shorter period from 12:00 to 21:00 today only.

conditions at start of forecast: variable wind direction at 5 knots, 4 Km vis in mist with some scattered cloud at 400 ft AGL and a cloud ceiling at 800 ft AGL.

They expect some temporary periods between 12:00 and 16:00 of 6 Km vis and no significant weather with a cloud ceiling of 1500 ft AGL.

They expect some further temporary periods between 16:00 and 18:00 of reduced cloud ceiling coming down to 400 ft AGL.

and then they expect the cloud cover to lower permanently between 18:00 and 21:00 to the 400 ft AGL.

So no mention of the fog or reduced visibility periods at the other two airports overnight yet as the forecast only covers up to 9 PM...

Hope this helps.