Actually deer in Richmond Park are not afraid of people. Other way around - you have to be careful. Deer are peaceful animals and in the park they so use to people, dogs and cars that some times you can forget they are wild. I used Fuji S7000 camera with standard lens. I zoomed a little bit from the distance of about 50m. I was lucky that deer been looking not at me with camera but at my wife (she was even closer).
Very nice image Saulius. The composition is very good, with the slanted horizon line and the trees behind it in the background, however I would have liked to maybe see a bit more of the sky, possibly tilting the camera up. This would maybe cause a problem with the gorgeous tuft of grass in the lower left foreground, so I'd suggest crouching down lower and taking the shot pointing upwards. Fantastic capture though, with the moment in time look on the deer's face. Brilliant.