Police confirmed that a residential address in the area had been evacuated and was being searched, but declined to say if the operation was linked to the suspect arrested. He has not been charged or identified.
It was the fifth terrorist attack in Britain this year, following a vehicular and knife attack near Parliament in March, a suicide bombing at a rock concert in Manchester in May, and a van and knife attack around London Bridge and a van attack outside a London mosque, both in June.
It is understood the device had a timer, but Frank Gardner, the BBC's security correspondent, said the bomb appeared not to have gone off properly.
Deputy Assistant Police Commissioner Neil Basu said it was a "significant arrest".
Liverpool vs Burnley, Premier League
OFFICIAL: Sean Dyche has confirmed that former Man United goalkeeper Anders Lindegaard is training with Burnley . Liverpool were relatively untroubled for most of the game, but they always find a way to stumble in matches.
"Everyone just piled out of the tube and there was a distinct smell of burning".
According to the Department of Foreign Affairs, about 182,700 Filipinos live in the United Kingdom, a majority or 70% in the Greater London area.
The explosion during Friday's morning rush hour also left several passengers fleeing in panic.
Mrs May said: "The public will see more armed police on the transport network and on our streets, providing extra protection".
"The rationale behind this request is to reduce numbers in crowded areas and will be applicable to all public events taking place this weekend".
Britain's terror threat level remains at critical - the highest level - meaning authorities believe another attack is imminent.
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