I hit a small deer on my Africa Twin, also in Essex, but further north than Epping. Luckily I was going fast so it hit its head on my crash bar, boots and footrest I think. If I had been going more slowly it would have been under my front wheel. Deer was killed outright when I u-turned and went back to look. It was pitch black so I had to point my headlights at it then walk to it and check. Hair and blood all down my swing arm when I got into my lit garage.
I reported it to the old bill just in case, no one was sure if it was a legally reportable animal or not, I think it depends on if it is wild or owned. I think the Epping ones are owned, but allowed to roam. Mine was a Muntjac which are descendants of escaped pets from the Victorian era I think.