Addressing the Royal United Services Institute, May revealed the arrest of an al-Qaida member for the first time, although she gave no details.
"He is alleged to have been planning a terrorist attack in this country. Threats such as these are likely to continue," she said.
During her remarks, May promised an overhaul of the country's counterterrorism laws. She said during a decade as opposition spokeswoman on security she engaged in "long and hard" thinking on the balance between personal freedom and security.
May said British police and intelligence agencies have been targeting associates of the Yemen-based al-Qaida group. It is believed to be responsible for the bombs found on U.S.-bound planes last week and for the failed underwear bombing over Michigan last Christmas.