Two people have been arrested in connection with the west London bombing, and Ms Rudd has announced the United Kingdom threat level was being downgraded.
The Islamic State militant group have claimed other attacks in Britain this year, including two in London and the pop concert in Manchester.
Following the 7/7 bombings in 2005, the government attempted to get the maximum period of detention without charge extended to 90 days, but the proposal was defeated in the House of Commons.
The "severe" level means another attack is highly likely but the higher "critical" level means an attack may be imminent.
British police said they had arrested two more men on Wednesday in connection with the bombing of a commuter train in London last week which injured 30 people, bringing the total in custody to five.
It followed the arrest of a 25-year-old man in the city on Tuesday night in a counter-terrorism raid.
The 18-year-old was arrested by police in the departure lounge of Dover ferry port, which is the busiest ferry hub in Europe and a gateway to the French coast, police said.
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Patrols by armed police were increased across the country following the Parsons Green tube attack on Friday.
"The arrest was carried out by officers from the Met's Counter Terrorism Command, supported by colleagues from Gwent Police and the Welsh Extremism and Counter Terrorism Unit (WECTU)".
Local media said the home belongs to a couple who have fostered hundreds of children, including refugees.
Members of Yahya's family confirmed to ABC News that the man in the video was Yahya but said they had not yet been contacted by authorities about his arrest.
Mayor of London Sadiq Khan said "significant" police activity would continue over the weekend and thanked police, adding: "They are there to keep us safe".
"It is inevitable that so-called Islamic State or Daesh will try to claim responsibility but we have no evidence to suggest that yet", she told the BBC. Health officials said none of the injured were in serious condition.
"It is necessary for us to look, as we are doing, at whether our police and security service have the full capabilities, the powers that they need", May said.