(ABC News) -- At least 20 patients were taken to area hospitals after London police responded tonight to two "terrorist incidents" following reports of a vehicle plowing into pedestrians on London Bridge as well as reports of stabbings at Borough Market.

In a statement, United Kingdom Prime Minister Theresa May confirmed the incidents are "being treated as a potential act of terrorism."

“This is a fast-moving investigation," she said. "I want to express my huge gratitude to the police and emergency services who are on the scene. Our thoughts are with those who are caught up in these dreadful events.”

The BBC is reporting that more than one person is dead in the London Bridge incident.

The London Ambulance Service tweeted: "Multiple resources attending an incident at #LondonBridge, please avoid the area." Transport for London also tweeted that the bridge was closed in both directions due to a "major incident."

Metropolitan Police also reported that they responded to a reports of stabbings in Borough Market, and after officers responded "shots have been fired."

Police also reported a stabbing incident at Vauxhall, though Transport for London tweeted that the Tube station there has since reopened. Police have since said that the Vauxhall stabbing is not connected to the incidents on London Bridge and at Borough Market.

Metropolitan Police tweeted a warning, telling people in the areas to run to safety, hide and then call police if it is safe to do so.

London Bridge is normally crowded on Saturday nights, and Borough Market is a popular area packed with bars and restaurants a short distance from the bridge.

President Donald Trump was briefed on the situation, according to the White House. According to federal law enforcement and national security officials, the National Security Council is monitoring the situation as are the appropriate elements of the FBI and Homeland Security. The situation was described as ongoing and dangerous.

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BBC reporter Holly Jones, who was on the bridge at the time, told the network several people were hurt after a white van swerved and hit a crowd of people while it was crossing London Bridge.

"A white van driver came speeding -- probably about 50 mph -- veered off the road into the crowds of people who were walking along the pavement," she told BBC News. "He swerved right round me and then hit about five or six people. He hit about two people in front of me and then three behind. I'd say there are about four severely injured people. They all have paramedics assisting them at the moment."

She said there were about four people severely injured and that some 20 armed police officers on the scene.

People in the area tweeted video and images of the scene, showing police responding and injured people being treated.

This is a developing story. Please check back for more.