May also said in televised comments that the terror threat level would remain at "critical".
Speaking ahead of her departure for a NATO summit in Brussels, May said she would "make clear to President (Donald) Trump that intelligence which is shared between our law enforcement agencies must remain secure".
May also said in televised comments that the terror threat level would remain at "critical" -- the maximum level -- after being raised on Tuesday following the attack in which 22 people were killed.
"The public should remain vigilant," she said, following an emergency ministerial meeting.
May said around 1,000 soldiers were assisting police "providing important reassurance ahead of a bank holiday weekend of busy events".
May said she would work with "international colleagues on defeating terrorism" at the NATO summit.
When she attends the G7 summit in Italy on Friday, she said she would head up a discussion on counter-terrorism "and on how we will work together to prevent the plotting of terrorist attacks".
"G7 and Nato will enable us to work more closely together as we work to defeat the evil of terrorism," she said, expressing gratitude for support and condolences from countries around the world.