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Animal attendant Donna Hurring said 346 cats and kittens had come in to the shelter between January and March.
As Christmas was usually the busiest time for the SPCA, the increase was unexpected and had "certainly never been this big".
On Easter Monday, 89 cats and kittens were on the premises; permanent housing only catered for 50.
A holding room for desexed animals was used to hold the overflow.
"It puts the strain on us," Ms Hurring said.
With minimal space, staff and food, it had become the shelter's "biggest dilemma", she said.
All dry food was donated through a sponsor, but there was a severe shortage of canned cat and kitten food.
"We don't get the donations we used to."
She encouraged those who could to give to the SPCA food bins in supermarkets, or directly to the haven.