The animal welfare charity set up the scheme in December 2021 in Lancashire as a result of financial pressures during the pandemic.
However, the coronavirus crisis coupled with the current cost of living increase has seen the need for the food bank increase now more than ever.
The scheme aims to reach 110 food banks by the end of next year to provide help to the public and reduce animal abandonment.
In the first quarter of 2022, the RSPCA distributed double the pet food from the previous year to help meet demand.
Inspector Emma Brook, who works across West Yorkshire, said: “We are in desperate need for pet food donations at the minute as the current demand for the food bank scheme is very high.
"Sadly, it seems as though the cost of living increase means that more people are struggling to afford to feed their pets and are relying on the food banks more and more.
“The scheme was set up because we understood that many people were falling on hard times during the pandemic and we wanted to make sure that those who were struggling could still stay with their pets whilst they got back on their feet.
“We are now bracing for an influx of abandoned pets or owners who have to give them up because they can no longer afford to keep them but we hope that through the food bank we will be able to provide some support to people and their much-loved pets.”
It comes as the RSPCA releases its inaugural report, in partnership with the Scottish SPCA - the Animal Kindness Index - which looks at the nation’s attitude towards animals.
The report, based on a YouGov survey of more than 4,000 UK adults, revealed that the rising cost of living and the cost of pet ownership could threaten our love for our pets, with 72 per cent of pet owners saying they think the cost of living will impact their animals, almost 70 per cent expressing concern that the cost of care was increasing, and a fifth worried about how they will afford to feed their pets.
The study showed cat owners seem to be most impacted and concerned about cost of living pressures.
In Yorkshire and the Humber, 67 per cent of people said that the cost of looking after their pet had become more expensive over the last 12 months, while 21 per cent said they were worried about being able to afford to properly care for their pet and 14 per cent said they were worried about the cost of feeding their pets.
The RSPCA is seeing an increase in rescued animals coming into its care with many centres already full and others close to capacity, at the same time as rehoming is slowing down and signs that more people are looking to give up their pets.
Research by the charity shows in April 2021 there were around 4,400 searches per month around "giving up pets" and in April 2022 this figure rose by 50 per cent to a high of 6,600.
So far this year, between January and May, the food bank scheme has delivered more than 100 pet food bundles to its partner food banks across the north of England - but more food is now desperately needed.
If you would like to support the scheme, pet food donations can be taken to the drop-off point at RSPCA Halifax, Wade Street, Halifax, HX1 1SN. It is open every day from 10.15am-4pm except Sunday, when it closes at 3pm, and is closed all day Thursday.
Please specify pet food for the food bank when donating or place in the designated storage containers where available. There is a particular need for wet cat and dog food, as well as small bags of cat and dog dried food of 5kg or below.