The charity's chief executive, Baroness Delyth Morgan said that earlier tests could prove to be "an enormous breakthrough".
"The best possible long-term effect of our findings would be to help women recognize that early detection and modern, personalized breast cancer treatment saves lives, and to encourage more women to get screened annually starting at age 40", Hendrick said.
Lives are likely to be saved by spotting these cancers earlier and the extra screening would not create a significant risk of healthy women getting needless treatment, researchers said.
"Over 335,000 women were diagnosed with new breast cancer in the United States in 2018", she noted, and "eight out of ten of these women have no family history of breast cancer".
Schnabel says women should know their breast cancer risk. In this screening, 35 invasive breast cancer tumors of small size were detected before they could reach the lymphatic nodes.
The study suggests an estimated 86,000 women in their late 30s would benefit from annual screenings.
Also, Baroness Morgan appealed to the United Kingdom government to shift the NHS screening programmes with the age of 35 to 39 for women who have a history of breast cancer.
For the study, experts led by a team at the University of Manchester, writing in the journal EClinicalMedicine from The Lancet, examined data for 2,899 women from 2006 to 2015. In unscreened women, just 45% (131/293) of breast cancers were detected when the tumour was 2cm or smaller in size and 54% (158/290) of cases had already spread to the lymph nodes.
The trial compared the results with a group of women aged 35 to 39 who were at increased risk but did not undergo screening.
Lead author Professor Evans described the results of the trial as "very promising".
Annual screening for younger women aged 35-39 who have a family history of breast cancer would be highly effective in detecting tumours earlier, a major United Kingdom trial based in Manchester has found. "While we anticipate new scientific advances that will further reduce breast cancer deaths and morbidity, it is important that women continue to comply with existing screening and treatment recommendations", he said.
"Breast cancer survival is at its highest ever and with improved screening a key focus of the NHS long term plan, even more cancers will be diagnosed earlier", she added.