In three years it has seen a 30 per cent hike in "abandonment calls" to its emergency line.
It suggests the cost-of-living crisis is largely to blame, with many owners unable to afford pet food and vet bills.
It also says pet ownership has soared since lockdown, with high numbers of "unsociable pandemic pups" being rejected because of their complex behavioural problems.
The charity released the figures as part of its Join The Christmas Rescue campaign, ahead of what is expected to be another bleak winter for thousands of animals.
The charity said the number of reported abandonments during 2020 was 16,118.
By last year this figure had risen to 20,999, with the RSPCA projecting it will hit 23,000 by the end of 2024 - a 42 per cent increase in four years.
It is urging potential owners to research before buying a pet and seek early treatment to prevent chronic illnesses escalating.
Animal centres across England warn they are struggling to stay afloat due to the costs of taking in rising numbers of abandoned pets.
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