Nothing to suggest you are witnessing anything out of the ordinary. A SVFR clearance requires the aircraft to be flown clear of cloud and in sight of the surface. The 500 foot rule applies, the 1,000 foot rule doesn't. The arrival and departure procedures from Battersea are well laid down. The aircraft will be in contact with Heathrow Special over that area and are tracked closely on radar, with a transponder code given. IFR aircraft have Mode C so the altitude shows up on the controller's screen. Due to the proximity of inbounds descending to LHR over that part of London, helicopters are given a maximum altitude to fly, i.e. not above 1,000 feet, London QNH. The route H3 to the west of Hammersmith carries a maximum altitude of 750 feet.
The northbound routing is not given to single engined aircraft.
Helicopters suffering a "catastrophic hydraulic failure"?
Helicopters have either no hydraulics (in which case the system can't fail), one hydraulic system (in which case the aircraft is flown in manual), or two hydraulic systems, in which case the warning light comes on (only amber, no catastrophe here) and the other system carries on powering the controls). The aircraft continues on its way.
I think you should be more worried about something like a Boeing 777 suffering catastrophic fuel system icing, running out of engines and landing short of the runway at Heathrow.
Btw, it isn't totally unheard of for helicopters to fly the ILS at LHR, totally in cloud, down to a 200 foot cloudbase. I don't see a difference in risk.