This is from the Cancer Research site:
Is there a link between breast cancer and the type of bra you wear?
No, there is no scientific evidence to prove this. There are a number of rumours that have suggested that bras cause breast cancer by obstructing the lymphatic system. The emphasis has generally been on under-wired bras. These sources claim that bras squash the fine tubes of the lymphatic system. The idea is that this stops the normal drainage of the breast tissues, causing toxins to gather in the breast and resulting in cancer. You would need to wear a bra that was painfully and unbearably tight to have any effect on your lymphatic system.
One source suggested that this theory explains the high rate of breast cancer in western cultures and the low rates in the developing world, where women are perhaps less likely to wear bras. There are no scientific studies that back up this claim. And there are many differences between Western and developing countries' lifestyles that could contribute to breast cancer risk. Much of the research in this area has concentrated on differences in diet between different countries and cultures.
Constriction or applying pressure to an area of the body does not cause normal cells to become cancerous. There is a lot of information about how cancer starts and grows in the 'About Cancer' section of CancerHelp UK.
We don't know exactly what causes breast cancer, but there are a number of well known risk factors. These include having a strong family history of the disease and getting older. There is a lot more information risks and causes of breast cancer, and possible protective factors in the Breast Cancer section of CancerHelp UK.