At least six people were killed and 30 others injured in two terror attacks at the heart of the UK's capital in which armed Scotland Yard officers shot dead three suspects.
The attacks that took place at London Bridge and Borough Market comes just days ahead of the general election on June 8.
May called the "terrible" events in London a "potential act of terrorism".
"Following updates from police and security officials, I can confirm that the terrible incident in London is being treated as a potential act of terrorism," May said in a statement.
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"Brutal and shocking incidents reported in London. My thoughts are with the victims and their families. Thank you to the emergency services," Corbyn said.
The first incident was reported at London Bridge when a van swerved off the road into a crowd of pedestrians, BBC reported.
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, an eye-witness was quoted by the report.
Within minutes, there were reports of a second attack at Borough market on the South Bank of the Thames where three men wielding knives 10 inches long began attacking passersby, even entering one restaurant to attack night diners.