Shock figures show the charity investigated 3,636 crimes last year – up from 3,459 in 2013.
In one of the cases last year, a woman who ran a cat rescue centre in Derbyshire allowed seven of the animals to die slow, painful deaths over a number of days.
The cats were shut in a dark shed with no comfort or veterinary intervention.
RSPCA Inspector Sarah Gardner said: “Despite taking public money to run the centre the cats were living in a totally unsuitable environment.
“The shed was in a disgraceful condition with seven wire animal crates containing dead cats.
“It was a shocking and pitiful sight that shocked the attending vet.
“While these animals were left bereft of any care or attention whatsoever, four surviving cats lived in her home.
“No water was available to them – when the kitchen tap was turned on all four cats instantly jumped up on the work surface and started drinking thirstily straight from the tap.”
The 26-year-old defendant – whose identity cannot be revealed by the RSPCA because of data protection laws – was banned from keeping animals for life.
Ms Gardner added: “When interviewed the woman showed no emotion to the photographs of the dead cats and was only concerned for the future of her own cats.”
Of the 3,636 animal cruelty cases in Derbyshire last year, 438 were deliberate acts such as beatings, poisonings and mutilation.
Nationally, the RSPCA investigated 159,831 animal cruelty complaints in 2014 – compared with 153,770 in 2013.
RSPCA chief veterinary officer James Yeates said: “It’s extremely concerning that we’re still receiving more than 20,000 complaints about animals being deliberately caused to suffer and that’s 20,000 too many.
“Most of the complaints we receive involve animals being neglected or not receiving the right care and often we can put that right by offering welfare advice.
“However, it’s shocking that in 2014 people are still being deliberately cruel in what can be disturbingly inventive ways,” he added.
The RSPCA, which receives a call for help approximately every 30 seconds, is the oldest and largest animal welfare organisation in the world.
It is one of the largest charities in the UK, with 1,453 employees.
Call the RSPCA on 0300 1234 999 to report cruelty or an animal in distress.