The move follows defeat for the UK government in January at the European Court of Human Rights. The court, which is not an EU institution, found that Section 44 violated the right to respect for private life; article eight of the European Convention on Human Rights.
May said: "The Government cannot appeal this judgment although we would not have done so had we been able."
"I can therefore tell the House that I will not allow the continued use of Section 44 in contravention of the European Court's ruling and, more importantly, in contravention of our civil liberties."
Police use of Section 44 to stop individuals will no longer be allowed, although it will still apply to vehicles.
The legal challenge against Section 44 was brought by Liberty, the human rights charity, following the stop and search of a peace protestor and a journalist who were planning to attend a demonstration against a large arms fair in London in 2003.
Liberty director Shami Chakrabarti hailed the withdrawal of the power today. "It is a blanket and secretive power that has been used against school kids, journalists, peace protesters and a disproportionate number of young black men," she said.
"To our knowledge, it has never helped catch a single terrorist. This is a very important day for personal privacy, protest rights and race equality in Britain."
Soon after taking power, the coalition launched a review of Section 44 which found police had gone even further than its powers allowed on 40 occasions. http://www.theregister.co.uk/2010/06/10/stops_search/
Today's announcement will be welcomed by photographers, who have battled police for the right to take pictures in public places in recent years. Often officers have used Section 44 to stop and search snappers when they are not suspected of doing anything wrong. ®