From late September until November, in the UK, it is rutting season for deer. During this time the deer, particularly the stags, are more active. I visited Richmond Park at the start of the season, on a overcast morning. The conditions were not ideal for photography, but it was rather beautiful wandering around the park in the early morning, just me, my friend and the wildlife.
I definitely recommend making time to visit the park and the deer, but please remember that they are wild animals and that during rutting season the stags can be aggressive (as we learnt when one charged at us after a lady scared it with her camera phone flash!).