SASless,
There are 2 Control Zones that cover the area of (Centralish) London:
The London Control Zone and the City Zone.
The former is Class A airspace and the latter is Class D. It is not clear to me at all times during the flight which of these 2 zones the helicopter was in: sometimes it would not be in either zone. [In the areas in the vicinity of Redhill and Elstree the helicopter would be in uncontrolled airspace below the London Terminal Manouevring Area (which starts at 2500ft)] Vauxhall Bridge and St George's Wharf are fairly close to the boundary between the 2 zones. My recollection (no chart to hand) is that they are both just in the Class D City Zone.
In Class A airspace IFR is the norm. VFR is not permitted and non IFR traffic may be permitted SVFR.
In Class D VFR and IFR are permitted, although non-IFR traffic may have to be SVFR in some circumstances.
The flight rules not only affect the visibility and weather limits but also the low flying rules that apply. For example, when under SVFR an aircraft is exempt from the 1,000 ft rule, but not when VFR.