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Metropolitan Police Commissioner Sir Ian Blair said the devices were set off across the city "almost simultaneously".
He added that the explosions were small and that police had the situation under control.
Reports indicate one person has been slightly injured in the incidents.
Police have said the incidents are not a serious as the July 7 attacks.
Passengers reported one blast at Warren Street station off Tottenham Court Road in central London.
There has also been an incident on a bus in Hackney, East London.
Stations at Warren Street, Oval and Shepherd's Bush have been closed.
Chemical searches at all four sites have proved negative.
There was also an incident involving armed police officers at University College Hospital in Bloomsbury close to Warren Street station
An internal memo to staff at the hospital warned them to be on the lookout for a black male, possibly of Asian origin, about 6ft 2ins tall, wearing a blue top with wires protruding from the rear of the top.
Police say the incident is now over.
Across London, a man was arrested at gunpoint by armed police at the gates of Downing Street.
Police evacuated pedestrians from Whitehall and Parliament Street, immediately outside Downing Street, and closed the roads to traffic.
Tony Blair said that although the incidents had to be treated as seriously, there had been no reports of casualties.
"We know why these things are done - they are done to scare people," he told a news conference.
He said police were working to return London to normal as quickly as possible.
Stations affected
Services on the Victoria, Northern and Hammersmith & City and Bakerloo Lines have been disrupted.
Warren Street tube passenger Ivan McCracken told Sky News he spoke to an Italian man who witnessed an explosion just after the train arrived at the platform.
"He told me he had seen a man carrying a rucksack which suddenly exploded. It was a minor explosion but enough to blow open his rucksack. Everyone rushed from the carriage. People evacuated very quickly. There was no panic."
At Oval station there were reports of a man dumping a rucksack in a carriage then fleeing as the doors closed.
Scotland Yard said emergency services responded to an "incident" on a Number 26 bus in Hackney Road, on a junction near Colombia Road, east London.
Bus operator Stagecoach said the driver heard a bang at around 1.30pm.
The bus had left Waterloo and was in Shoreditch when the incident happened.
It is two weeks to the day since bombers attacked three Tube trains and a bus in central London.