You can also park in the cafe car park. The cafe is called The Pheasantry and can be seen on Google Maps at the link below. You drive up Chestnut Avenue, turn left, then left into the car park. The cafe isn't particularly cheap but the food is OK. It's open until 6pm at the moment, 5pm from the end of October.
If you want to take a break from the deer (and the lakes and wildlife, of course - Heron Pond and Leg of Mutton Pond), go out of the back of the cafe into the Woodland Garden. It's quite long and in two sections going north-east towards Cobbler's Walk, and has a few interesting features such as ponds with bridges and flower beds, and a totem pole.
Above all, as Retune said, "WATCH OUT FOR TICKS!" (caps mine)
This can't be stated too often. Lyme Disease can be life-changing. You can go from being a photographer to bed-bound in a few weeks and, in some cases, encephalitis can result. The ticks aren't only on the deer, either, but can be transported by dogs and squirrels. If you plan on more than one visit, get a tick kit and learn how to use it.
Map showing The Pheasantry
https://www.google.co.uk/maps/place...256f459718!8m2!3d51.416531!4d-0.3398173?hl=en
Tick kits on Amazon
https://www.amazon.co.uk/s/?ie=UTF8...argid=kwd-302419151275&ref=pd_sl_2fcs0gs2nd_e