The #DareToBare campaign, which is backed by Leeds-based PR firm MacComms and crowd-funding platform Swoosch, challenges people to take a topless selfie, covering the breasts or chest, and donate to the Swoosch fundraising page.
Participants are then expected to post their selfie and a screenshot of their donation to social media and tag three friends to ensure the challenge is continued.
The campaign, which will run until £10,000 has been raised, was launched on International Women's Day (8 March) to mark the two-year anniversary of Kirke's double mastectomy operation, following her breast cancer diagnosis in 2013, MacComms said.
Kirke said: "When doctors told me I had a lump in my right breast, I decided I wasn't going to become a victim. I took the decision to have a double mastectomy to prevent going through this again and I want to encourage more women and men to check their breasts so they don't have to go through what I have, or worse."
At the time of publishing, Kirke had raised just under £210.
A spokeswoman for MacComms, which is providing social media and PR support for Kirke's campaign, said #DareToBare had received no negative publicity.
Cancer Research UK, which recorded reveunes of £634.8m in 2015, was the largest UK charity by income last year, according to PRWeek sister title Third Sector.
Critics for similar campaign
Last year a similar campaign went viral, calling on social media users to post a black and white selfie with the caption "challenge accepted". The campaign was designed to raise cancer awareness, but faced a backlash with cancer survivors and other commentators criticising the initiative.
Rebecca Wilkinson, who, like Kirke, also had a double mastectomy, said the challenge did nothing to promote cancer awareness.
