"The increase in the threat level is related to developments in Syria and Iraq where terrorist groups are planning attacks against the West," May said.
"Some of those plots are likely to involve foreign fighters who have travelled there from the UK and Europe to take part in those conflicts."
The "severe" threat level means an attack is "highly likely", although May added there was no intelligence to suggest that an attack was imminent.
Prime Minister David Cameron was due to make a statement on the raising of the alert level at 0615 IST.