Certain things are becoming clear about this accident. The pilot was highly skilled and experienced and regarded by other helicopter pilots as one of the best in the UK. The helicopter was twin engined and state of the art. As a twin engine copter can maintain altitude if one engine goes U/S, they are permitted to fly over London without following the river as is required for single engine helicopters. Because Heathrow controls most of the airspace over central London, any aircraft that needed to climb into such airspace to achieve a safety altitude would need permission to do so.
Freezing fog can be treacherous, with two weather systems colliding the cold air will push under the warm air, which can cause the fog which might have been lurking at one level to surprise anyone who had relied on a weather observation of only a short time before.
But to turn off the warning lights at daybreak on a spindly crane would render it just about as easy to see as power cables strung across a valley; that is, invisible until too late. It must be possible to require these structures to be made more conspicuous at any time of day. Large orange plastic balls are strung on wires to make them easier to see. Strobe lighting is used on aircraft to call attention to their approach. Anything that sticks up that high over London and is inadequately lighted in our gloomy winter weather, is asking for trouble.