The animals both died and a third is recovering after it is thought to have ingested anti-freeze. None of the incidents are thought to have been deliberate.
The pets all lived on the same street in the town, Brookland Road, and the charity is now advising people to ensure dangerous chemicals are kept securely locked away.
RSPCA inspector Claire Little was informed of the deaths three weeks ago and the cats have since been given blood tests to determine the cause of the poisonings.
“There’s no evidence that these incidents were deliberate, but it just goes to show that accidents can have fatal consequences,” she said.
“It is extremely important that people take proper care when using substances which could innocently be eaten by domestic pets.
“All of these incidents could have been avoided. The owners of all of these cats are understandably absolutely devastated.
“With winter just around the corner I wanted to remind people to make sure all potentially harmful substances are kept safely away from inquisitive pets.”
Signs of poisoning can be seen anything from 30 minutes after a cat has ingested the chemical, though it can be two or three days before signs of kidney failure are seen.
Symptoms to look out for include vomiting, the cat seeming depressed, sleepy or unco-ordinated, seizures and breathing difficulties. In many cases, the animal’s organs are too badly damaged for its life to be saved even with veterinary treatment.
If you suspect that your cat has been poisoned you should take it to a vet immediately. If possible, you should take a sample of what the cat has eaten or drunk, or the container.