The animal rights charity worries that financial fallout from the pandemic will mean more owners struggle to keep their pets.
June, July and August of last year saw the RSPCA called to a total of 218 cases of abandonment in Swindon and across the rest of Wiltshire.
The national total for the period was 16,519.
Abandonment typically peaks in the summer months, but the impact of COVID-19 means the charity is bracing itself for a higher total than usual.
During the three months since lockdown began, the RSPCA has received reports about 3,492 abandoned animals - about 40 calls a day - including 1,509 dogs, 1,165 cats, 299 small animals such as hamsters, guinea pigs and ferrets and 275 exotic pets.
Some have been abandoned deliberately, while others were left because their owners became ill.
Dermot Murphy, head of the RSPCA’s animal rescue teams, said: “During lockdown we’ve seen pets become a source of comfort and support for people and it appears many people have taken on new animals.
"Fortunately during this time we’ve dealt with fewer abandoned pets. However, we are worried that as lockdown eases, people return to work, go on holidays or struggle financially we will be facing a massive surge of animal abandonments.
“Sadly summer tends to bring with it a surge in abandoned animals. We don’t know why but it may be a combination of the warmer weather making people feel less guilty about dumping a pet to fend for themselves and people doing away on holiday abandoning pets instead of arranging care for them.”
RSPCA rescue teams have been working throughout lockdown after being classified as essential key workers.
Dermot said: “This is the toughest year yet for the RSPCA. Despite the huge challenges, our amazing teams have been continuing to rescue animals throughout this crisis.
“I’d urge anyone struggling with their pet to ask for help. Animals have been there to help us through the crisis - please don’t abandon them now.”
The charity's advice for anybody struggling to look after their pet includes seeking help from friends and loved ones, asking vets about payment plans for certain treatments and getting in touch with local rehoming charities.
The RSPCA website is https://www.rspca.org.uk/