“This cannot be a time when any of us allow competition between partners, rigid institutional restrictions or deep-seated ideology to inhibit our cooperation and jeopardize the security of our citizens,” she said.

Mrs. May said she wanted the security pact signed fast, even before negotiators agreed on the Brexit deal. “We shouldn’t wait where we don’t need to,” she said.

The prime minister also offered one big concession that might prove controversial at home. When cooperating with European agencies, Britain would “respect” the jurisdiction of the European Court of Justice, she said. Hard-line advocates of Brexit have argued that Britain should take back control of its laws and judicial system and no longer be beholden to the rulings of the European court.

It is the latest self-imposed red line that Mrs. May has quietly crossed as Britain races against the clock to extricate itself from four decades of close cooperation with the 28-member bloc. She has conceded almost everything European negotiators have demanded in the first phase of talks, from a divorce settlement of 39 billion pounds (about $55 billion) to a transition period in which Britain will keep to European Union rules even after it legally quits the bloc.

“Another red line has gone pink,” said Mark Leonard of the European Council on Foreign Relations.

But for all of Britain’s tortured wobbles in the Brexit negotiations, it has leverage on defense, and many here paid close attention to Mrs. May’s speech.