The total number of arrests in the case has increased to six.
Scotland Yard's Counter-Terrorism Command investigating the attack arrested the 25-year-old from Newport.
Earlier, an 18-year-old man was arrested in the port area of Dover. None of the suspects have been named.
The incident took place at the Parsons Green station, which has been closed.
"I never think it's helpful for anybody to speculate on what is an ongoing investigation," May said.
Flowers, posters and images were placed at the gates of Kensington Palace.
Scotland Yard has launched an investigation after a 26-year-old man stopped his car and then wielded a large knife.
Laila Rouass, 46, who was on a holiday in the city with her 10-year-old daughter Inez Khan, live tweeted from her hideout as the attack unfolded in the busy Las Ramblas area of the city.
Sentencing the men, Justice Globe said the men had been gripped by a "long-standing, radical, violent ideology".
While his official diary of engagements come to an end on Wednesday, the Palace has said the Duke may still decide to attend some events alongside the Queen.
All the three, aged between 25 and 33 are believed to be of Pakistani origin
The next hearing to assess the progress in the case will be held at Westminster Magistrates' Court on September 14.
The liquor baron showed up despite being exempt from appearing by the judge at the last hearing on June 13.
The rally was being planned by UK-based Kashmiri groups to mark the first death anniversary of the commander of the Hizbul Mujahideen terrorist outfit killed in a gun battle with Indian armed forces in the Kashmir Valley on July 8 last year.
A rare sketch by John Henry Amshewitz and correspondence to Sarat Chandra Bose will go under the hammer at a Sotheby's auction on July 11.
The MPs voted in favour of the Queen's Speech by 323 votes to 309 with a majority of 14.
Residents of 650 flats in four tower blocks on an estate in the Swiss Cottage area of north London were evacuated on Friday night by the local Camden Council, following tests ordered in the wake of the Grenfell Tower blaze on June 14, which claimed at least 79 lives and displaced hundreds others.
According to witnesses, Osborne shouted, 'I want to kill all Muslims' as he drove into a crowd.
The British government has also ordered an examination of Hotpoint's Fridge Freezer units following the Scotland Yard's statement
Under the deal, Lockheed will shift its Fort Worth, Texas plant to India without directly affecting American jobs.