Breast scans are thought to save lives
Part of the reason for the increase may be that women are chosing to have a family later in life as pregnancy is thought to guard against the disease.
There are now an estimated 39,500 new cases of breast cancer diagnosed in the UK every year, according to the Imperial Cancer Research Fund and the Cancer Research Campaign.
The shift is remarkable since breast cancer occurs almost entirely in women whereas lung cancer affects an estimated 38,900 men and women.
Experts know that the overall decline in the number of new lung cancer cases reflects the falling number of male smokers over the last 50 years.
Baffled
Sir Paul Nurse, Director General of Imperial Cancer Research Fund, said: "The good news is that, despite the increase in the number of new breast cancer cases, survival rates continue to improve and over 70% of women are now successfully treated.
"A number of lifestyle factors may also be contributing to breast cancer trends.
"For example, more British women are choosing to have their children later in life and doctors are reporting an increase in obesity - in post-menopausal women this is a risk factor."
Breast cancer, like most cancers, is largely a disease of older age, with around 80% occurring in post-menopausal women.
Lung cancer, however, is generally a consequence of smoking, with up to 90% of cases related to tobacco.
Female smokers
Although the number of people diagnosed with lung cancer is falling, this masks the fact that cases are continuing to rise among women.
Professor Gordon McVie, director general of the Cancer Research Campaign, said: "Women didn't take up smoking in large numbers until the 1960s and, because lung cancer takes 20 to 30 years to develop, we're only now seeing its deadly impact.
"The figures for these two cancers mask a North-South divide with breast cancer being more common in the affluent South and lung cancer still dominating in Scotland and the far North of England.
"I wish I could offer a magic formula for preventing breast cancer, but unfortunately there isn't one.
"However, by being breast aware and going for screening, it's more likely that the disease will be detected early when there is a 90% chance of survival.
"Smokers, on the other hand, have it entirely within their power to reduce the lung cancer toll."
Delyth Morgan, chief executive of the charity Breakthrough Breast Cancer charity, said there were a number of factors affecting the likelihood of women developing breast cancer.
She said: "Women's lives now are so different to how they used to be.
"Two generations ago my grandmother had 12 children, women aren't going to start having 12 children now.
"But there are other factors too. The whole 21st century lifestyle is very different, and I don't think scientists understand properly what all the factors are in there conspiring to make this increase happen."