With regard to VFR and SVFR. The determination of whether a pilot can comply with the minima for operation in VMC lies with the pilot. There are specific limits applied for aircraft operating in a control zone VFR or SVFR inbound or outbound from an airfield.
However when transiting a control zone, in general the requirement for a helicopter operating in class "D" airspace below 3,000ft amsl, the pilot must operate in sight of the surface and with a minimum inflight visibility of 1,500m. It lies with the pilot to determine if he has that flight visbility. Regarding the in sight of the surface point, I believe that all METARS in the area the the pilot was flying reported a broken cloud base. Given that broken is anything from 5 oktas to 7 oktas, it is possible that the pilot could see the surface even when he was "good VMC" on top - the pilot never said it was an undercast.
More evidence on this is when the pilot reported that he could see Vauxhall bridge, at this time the pilot was in sight of the surface.
The UK AIP gives weather minima for various zones etc, one point in the Heathrow entry (EGLL AD2.2) is that to operate in the CTR on a heli route the minimum vis to do so is 1,000m.