The Honourable Artillery Company is based at Armoury House, on City Road (the continuation of Moorgate heading north). The do indeed have a 'big patch of greenery' which, aside from parades, gets used for corporate events and the odd game of cricket.
Evening of 20 May, they had a recruiting 'open day' and had a Chook drop five bods in. 'twas a hairy jump as it was a bit breezy, but from my vantage point they all looked to make target.
The Chook flew overhead the HAC then headed up Dalston way, before doing a right-hander, back over Clerkenwell and a left into the breeze to drop the team; then headed south-west.
The HAC often gets medium-sized choppers (eg. up to Puma size) in; I'm not sure if the Chook landed on 20 May, it could in terms of area but it might kick up enough dirt to annoy the neighbours.