Of the three bird statues in the park, the two smaller ones - worth around £2,000 each - were taken between 4.30pm on Thursday (May 7) and 8am on Friday (May 8).
The larger statue has been left behind.
Officers at Feltham police station have said a suspicious blue pick-up truck, possibly a Ford Transit, was in the car park at the time and may be connected to the incident.
This is the second criminal attack on the fields in the past month, following the brutal killing of two newborn lambs on April 10.
The unique figurines of Bitterns - a rare bird which can be found in the park - were each carved from a single tree trunk and were gifted to the park.
They were taken from the overflow car park at the Clockhouse Lane entrance.
Officers have urged anyone who may have been in the park at the time or seen anything suspicious to get in touch.
Anyone with information should contact 0208 247 6321. Crime reference: 0509168/15.