Not sure it was a case of not being informed about the crane. The air navigation order would have required the pilot to remain 500 feet clear of any "person, vessel, vehicle or structure" and 1000' clear of any "built up area or organised assembly of people" with the ability to glide clear in the event of engine failure. An exception is made for taking off and landing.
That's assuming decent visibility, too. I'd expect MUCH wider margins to be used in fog!
I would regard London, with the exception of the Thames, as a built up area, so, if he was flying at less than 1000' above the building, he planned to be over the Thames.
Unless the crane extended significantly more than 500 or 1000 feet from the building, depending on your viewpoint, its' presence shouldn't have been material because the pilot wouldn't have been planning to fly that close to the building.
I reckon he was simply flying in very low visibility and wasn't where he intended to be.

A tragic event, and sympathies to those killed and injured. It could have been very much worse, however.
It does make me wonder how wise it is to allow non-emergency aircraft to operate that low over a city in instrument conditions, though.