An 18-year-old man has been arrested by Kent police in Dover under section 41 of the Terrorism Act.
The man is expected to be transferred to a London police station.
The arrest came as Britain deployed hundreds of soldiers at strategic sites on Saturday to free up police to hunt those behind a bomb which injured 29 people on a packed commuter train in London and triggered the country's highest security level.
Prime Minister Theresa May said the critical threat level meant an attack may be imminent, after a bomb engulfed a carriage in flames and sparked a stampede during the Friday morning rush hour in west London.
Meanwhile, US President Donald Trump controversially tweeted: 'Another attack in London by a loser terrorist.These are sick and demented people who were in the sights of Scotland Yard. Must be proactive!'
Another attack in London by a loser terrorist.These are sick and demented people who were in the sights of Scotland Yard. Must be proactive!— Donald J. Trump (@realDonaldTrump) September 15, 2017
The Prime Minister Teresa May responded to his tweet by saying such speculation was 'not helpful'.
The home-made bomb, which apparently failed to detonate properly, was the fifth major terrorism attack in Britain this year and was claimed by Islamic State. The militants have claimed other attacks in Britain this year, including two in London and one at a pop concert in Manchester.
The attack at Parsons Green tube station prompted the government to take the rare step of deploying soldiers.
'For this period, military personnel will replace police officers on guard duties at certain protected sites,' May said in a televised statement.
'The public will see more armed police on the transport network and on our streets providing extra protection. This is a proportionate and sensible step which will provide extra reassurance and protection while the investigation progresses.'
The bomb struck as passengers were travelling to the centre of the British capital. Some suffered burns and others were injured in a stampede to escape from the station, one of the above-ground stops on the underground 'Tube' network. Health officials said none was thought to be in a serious condition.
Pictures taken at the scene showed a slightly charred white plastic bucket in supermarket shopping bag on the floor of a carriage with wires coming out of the top.
'I was on the second carriage from the back. I just heard a kind of 'whoosh'. I looked up and saw the whole carriage engulfed in flames making its way towards me,' Ola Fayankinnu, who was on the train, told Reuters.
'There were phones, hats, bags all over the place and when I looked back I saw a bag with flames.'
Britain's most senior counter-terrorism officer Mark Rowley said late on Friday that the investigation was progressing well.
'We are chasing down suspects,' he said. 'Hundreds of police officers are pursuing numerous lines of enquiry, trawling through hours of CCTV footage and speaking to witnesses.'
Source: Reuters and police updates