The 21-year-old was named by British media, who said he was originally from Syria and had been working at a fast food chicken restaurant. Islamic State militants have claimed credit for other previous attacks, including two in London and one at a concert by American singer Ariana Grande in Manchester.
"A significant amount of activity has taken place since the attack on Friday", said Dean Haydon, the Metropolitan Police's head of counterterrorism command.
She said the press office would not ordinarily provide this detail on a live investigation.
Police are continuing to search a house in Sunbury-on-Thames - home to Penelope and Ronald Jones, aged 71 and 88 respectively, who previously received MBEs for services to children and families.
The Wales arrest widens the police probe which detained two suspects in England on Saturday.
Islamic State militants said they were responsible for the attack although both British and US officials have cast doubt on the claim, saying there was no evidence any recognized militant group had ordered or organized the bombing. Dave Solway, who lives opposite Mr and Mrs Jones, said he saw the property being "swarmed" by police during Saturday's raid. The man was seen on camera leaving a house which police later searched.
Google's payment app Google Tez goes live
To make it easier for customers, the USA firm is also offering a Google helpline number and chat support on a daily basis. Tez works with all major Indian banks and the vast majority of smartphones - so you can pay or get paid by nearly anyone.
Pictures have today emerged of a 25-year-old man being arrested by a group of police officers last night, before the two arrests took place at a separate address just after 5am.
A third man has been arrested in connection with the Parsons Green terror attack, Scotland Yard said.
Thirty people were injured when the improvised device exploded during rush hour at Parsons Green station, with all but one now discharged from hospital. On the same day another person was arrested in connection to the attack in the west London suburb of Hounslow.
Authorities have reduced the terror threat level from "critical" to "severe", meaning they no longer believe another attack is imminent.
An 18-year-old man, understood to be the suspected bomber, and a 21-year-old man remain in custody after being arrested by police on Saturday.
The Terrorism Act allows police to detain suspects without charge beyond the four days allowed for suspects connected to other crimes.