It has been claimed that the reduced visibility itself is causing the problems, (http://news.bbc.co.uk/1/hi/uk/6200527.stm). To some extent, this makes obvious sense. Unless my understanding is out-of-date, there are basically four main controllers in tower control at Heathrow: the Ground Movement Planner (GMP), the Ground Movement Controller (GMC), the Air Controller (Departures) (Air D), and the Air Controller (Arrivals) (Air A). The GMP is responsible for the sequence and timing with which departing aircraft are cleared to start their engines; the GMC is responsible for clearing departing aircraft to receive a 'push-back' tow from a tug onto a taxiway, and for directing incoming and outgoing aircraft along taxiways, to and from the runways; Air D is responsible for the timing and sequence with which aircraft are cleared to take-off from the departures runway; and Air A is responsible for clearing aircraft to land on the arrivals runway.
Now, the aircraft themselves can land in foggy conditions without undue difficulty, but foggy conditions do pose a problem for the GMC, who normally observes the movement of the aircraft out of the window of the control tower. Note, however, that the GMC also utilises the Surface Movement Radar (SMR), which should be independent of foggy conditions, and the GMC operates at night-time, albeit with the help of a 'lighting operator', who controls the pattern of lights along the taxiways.
I have heard it claimed that the main problem at Heathrow lies not only with the surveillance capability of the GMC in the fog, but with the quality of the radio telephony in these conditions. If radio communication between the pilots and controllers is being distorted by the foggy conditions, then obviously this is a good reason for increasing the separation between aircraft.
Sadly, BAA have not considered using a FIDO system to clear the fog away from Heathrow, http://en.wikipedia.org/wiki/FIDO_(device). This was a British World War II system which ran pipelines down either side of a runway, with burners located at regulated intervals. Fuel would be pumped down these pipelines, and ignited at the burners to clear the fog!