Officers said interfering with swans in the wild without a lawful reason is an offence under the Wildlife and Countryside Act 1981 and could lead to prosecution.
The force reassured residents that local officers regularly patrol the area, but urged the public to remain vigilant.
Anyone who witnesses activity they believe may place wildlife at risk is asked to contact police on 101.
Police also reminded residents that injured or distressed wildlife should be reported to the RSPCA by calling 0300 123 8960.