In fact the usual clearance given at the moment is "The 133 radial to Brent, not above 1500' and then not above 1000' Heathrow QNH Brent to Battersea avoding R157."
If you want to fly tight to R157 then Brent to the Westfield Shopping Centre then to Earls Court brings you close to the boundary, but you do get closer to Hammersmith which is possibly why BFA is seeing more helicopters. Also with cloud at 1000' and all the city buildings a ground observer may be hearing "reflected sound" where the aircraft seems to be in one direction, but is in fact different place and therefore can't be seen when the ground observer looks for it.
Last week the weather was on the limits for Battersea, the slant range was good, but the horizontal range c***. I did wonder if anyone on the ground would have been able to see my aircraft, when my view of the London streets below was fine.
As for bimbling around in cloud at 500' the risks to career would be too great to take a chance on getting caught.
Finally most PPLs let alone fixed wing tend to be surprised at the level of kit we have in modern twins. Auto-pilots, couplers, amazing moving maps, sat- phones and a single engine performance that is better than the singles we originally trained on.
God we're mollycoddled today (Just no-one tell my boss
)