Animal Aid will place advertisements in national newspapers calling on the public to stop donating to four major medical research charities until they pledge to "end their funding of animal experiments".
The animal welfare organisation will ask the public to "withhold all financial support" from Cancer Research UK, the British Heart Foundation, Parkinson's UK and the Alzheimer's Society until they give such assurances.
The Victims of Charity report from Animal Aid alleges that "charity-funded" medical researchers have "deliberately damaged monkeys' brains with toxic chemicals, and slowly and systematically destroyed dogs' hearts".
It also claims that researchers have "tormented mice in water mazes", injected them with cancerous tissue, and used animals that had been subjected to special breeding programmes that left them "weakened, disease-prone and mentally deranged".
The report says the organisation's experts have assessed scientific reviews in specialist journals and concluded that animal-based research into cancer, dementia, heart disease and Parkinson's has been "a wasteful and futile quest."
The campaign will be backed by a series of national newspaper advertisements, as well as by campaign postcards that the public will be asked to fill in and send to the chief executives of the four organisations.
Andrew Tyler, director of Animal Aid, said: "The British public do not like the idea of animals enduring great suffering to no purpose – and Victims of Charity argues that this is precisely what is happening. Our high-profile campaign will put the charities under a great deal of pressure to rethink their research strategy."
A Cancer Research UK statement said research using animals was an "unavoidable part of our efforts to beat cancer".
"It's a legal requirement in this country that all new drugs (not just cancer drugs) are tested in animals before they're given to patients, to make sure that they're safe to use," it said.
"In a perfect world, animal research wouldn't be necessary. But cancer kills over 400 people every day in the UK, and all our work is aimed at reducing this death toll."
Peter Hollins, chief executive of the British Heart Foundation, said many adults and children were only alive today thanks to "pioneering treatments" that wouldn't have succeeded without involving animals.
"It's not a decision taken lightly, but there is sometimes simply no alternative," he said.
"Funding applications go through a rigorous review and we always actively encourage the use of alternative research methods. If this type of research is absolutely necessary, we demand the highest standards of welfare and follow strict Home Office guidelines."
A Parkinson's UK statement said: "A small but vital part of our research involves the use of animals. This is rigorously controlled by UK legislation and closely monitored by Home Office inspectors."
It added that, as a member of the Association of Medical Research Charities, Parkinson's UK is committed to "reducing the number of animals used in experiments, replacing their use with alternative methods where possible and refining techniques to maximise welfare".
Jeremy Hughes, chief executive of the Alzheimer's Society, said funding research was an essential part of the charity's work. "The majority of our research programme does not involve animals, and where there is no alternative we use only maggots, fruit flies, mice and rats," he said.
"Our researchers are bound by animal welfare rules, which are the strictest in the world."