Thanks to the finder, Spencer Neal, for the following:
"The bird was still present when I left. The park is scheduled to open at 8am tomorrow due to the early morning deer cull currently taking place: that said they opened the gates early at 7.30am this morning, which was when I went in today. There is a carpark at the entrance to the park, which is on the Hampton Wick end of the road from Kingston to Hampton Court Palace. I would suggest parking here and walking. Follow the road from the entrance car park heading for the golf club, ignoring the pond on the right (Hampton Wick Pond). You will come to a'crossroads' with Long Water immediately on the right (leading to Hampton Court Palace) and the small Overflow Pond next to the road on your left. Walk left, on a road towards the farm/stable buildings and between the Overflow Pond and the golf club in the distance, on your right, is Rick's Pond. Rick's Pond is much larger than Overflow Pond. The Grey Phalarope was on the side of the pond near to this road to the farm/stable buildings."