A third man has been arrested over Friday's Tube attack in Parsons Green.
The 25-year-old was arrested in Newport, south Wales, on Tuesday evening, Scotland Yard said. An address in Newport is being searched.
On Saturday an 18-year-old man, who the BBC has learnt had previously been referred to an anti-extremist programme, was arrested in Dover port.
A 21-year-old man was also arrested in Hounslow, west London. Both are still in custody.
A homemade bomb partially exploded in a train at Parsons Green station, injuring 30 people in rush hour.
The 25-year-old was arrested under section 41 of the Terrorism Act.
The arrest was carried out by the Met's Counter-Terrorism Command, supported by Gwent Police and the Welsh Extremism and Counter-Terrorism Unit.
Metropolitan Police Commander Dean Haydon said: "This continues to be a fast-moving investigation.
"A significant amount of activity has taken place since the attack on Friday.
"We now have three men in custody and searches are continuing at four addresses."
The 18-year-old arrested man is thought to have lived in a foster home owned by Ronald and Penelope Jones in Sunbury-on-Thames.
He is thought to have moved to the UK from Iraq aged 15 when his parents died.
The BBC has learnt that he had been referred to an anti-extremist programme before his arrest.
It is not known who made the referral and when - or how serious the concerns were.
Sources did not name the flagship Prevent programme, but it is thought that this is the mostly likely case as the referral for help was at local authority level.
Prevent is managed and delivered locally by multi-agency teams of social workers, police officers and other specialists.
He was already in contact with social services because of his foster care placement.
The 21-year-old man, believed to be Syrian-born Yahyah Farroukh, was also arrested on Saturday.
Mr Farroukh worked at Aladdins chicken shop in Hounslow, and has been described as a former foster child who had lived in the Jones's house.
Mr Farroukh posted a picture on his Instagram page in May this year with a suitcase on Cavendish Road, Sunbury, almost directly outside the Jones's house.
The properties already being searched are the Jones's house in Sunbury, Mr Farroukh's house in Stanwell, and Aladdins chicken shop.
At 08:20 BST on Friday a homemade bomb, which was transported in a Lidl bag, partially exploded in a Tube train at Parsons Green station, causing burns to a number of victims.
BBC News has obtained CCTV footage showing a person leaving the property in Sunbury carrying a Lidl bag at 07:04 BST on Friday morning.
It has also established more precise details of the suspect's movements: The man carrying the shopping bag then took the 07:15 BST train to Wimbledon, which arrived at 07:46.
After leaving the train he spent 20 minutes in the station toilets, before joining the District Line towards central London.
Detectives believe the suspect got off four stops later at Putney Bridge, which is one stop before Parsons Green station where the homemade bomb caught fire minutes later.