There are about 8,000 women diagnosed with triple-negative breast cancer in the UK each year, the charity said.
It is a less common but often more aggressive type of breast cancer that disproportionately affects younger women and black women, the organisation added.
Armstrong, a consultant medical oncologist and honorary senior lecturer, said: “Our earlier research has suggested that aspirin can make certain types of immunotherapy more effective by preventing the cancer from making substances that weaken the immune response.
“Anti-inflammatory drugs like aspirin could hold the key to increasing the effectiveness of immunotherapy when used at the same time. Trialling the use of a drug like aspirin is exciting because it is so widely available and inexpensive to produce.
“We hope our trial will show that, when combined with immunotherapy, aspirin can enhance its effects and may ultimately provide a safe new way to treat breast cancer.”
Dr Simon Vincent, the director of research, support and influencing at Breast Cancer Now, said: “The 8,000 women diagnosed with triple-negative breast cancer in the UK each year face the frightening reality of limited treatment options – we urgently need to address this.
“Research has already suggested aspirin could improve outcomes for many cancer patients and we hope that Dr Armstrong’s trial will show the same to be true for patients with triple negative breast cancer, so that we can prevent more lives being lost to this devastating disease.”
Breast Cancer Now said the pharmaceutical firm Pfizer had provided the charity with funding through an independent medical research grant and given its researchers access to several Pfizer medicines.