They are a 25-year-old arrested in Newport on September 19, a 30-year-old detained in the city the following day, and a 20-year-old arrested in the capital Cardiff on Monday.
Searches are continuing at a Cardiff address in connection with the attack at Parsons Green station in west London on September 15, which left 30 people injured.
Ahmed Hassan, 18, was charged on Friday with attempted murder and the malicious use of explosives likely to endanger life.
He is due to appear at Britain’s central criminal court in London on October 13.
No one else remains in custody.
The improvised device was placed on a packed train during morning rush hour. Despite apparently malfunctioning, it caused panic among commuters and some were hurt in a stampede as people fled the scene.
The Tube bombing was the fifth terror attack in Britain in sixth months — four of them in London and one in Manchester — with the bloodshed claiming 35 lives.
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