The interesting thing here is that City is Class D - and therefore only gives Special VFR in IMC. And we don't know if your site is in a "congested area" - some of that part of SE London is definitely non-congested.
And another complication: there's a lot of interest in helicopter activities around Blackheath at present. The area is a World Heritage site and the Blackheath Society have been successfully lobbying to get the unnofficial "Blackheath hold" removed from H4/IoD procedures.
CAA Flight Ops are aware of this.