A white van hit pedestrians on London Bridge on Saturday, then three men got out and stabbed people in nearby Borough Market resulting in 7 dead and 48 injured, according to BBC reports.
BBC reporter Holly Jones, who was on the bridge, said the van was "probably travelling at about 50 miles an hour" and hit "five or six people".
The three men who jumped out and started stabbing people were wearing fake bomb vests.
One witness told the BBC he saw a woman being stabbed "10 or 15 times" by men shouting "This is for Allah".
The three attackers were shot dead by police.
Several arrests have been made following a series of police raids in east London.
It is the third terror attack in the UK in three months, following the car and knife attack in Westminster in March, which left five people dead, and the Manchester bombing less than two weeks ago, in which 22 people were killed.
Most political parties have suspended national general election campaigning, but Mrs May said full campaigning would resume on Monday and the general election would go ahead as planned on Thursday.