"Heathrow radar is accurate enough to tell you that you are 100m off the route. Trust me, they told me!"
Given that the crane's about 50m from the river that's not accurate enough to keep out of trouble here. Actually, on a wider point, given that helicopter route H4 (east of Battersea) is presumably bi-directional, how do you ensure separation of incoming and outgoing traffic? Is there a convention that you fly on the left hand side of the river? If so, you're even closer to the crane.