Officers arrested a 24-year-old British man of Pakistani origin in the western town of Gloucester and said explosives have been seized from his home.
A security source told journalists on Thursday the arrests could prove to "be pretty big".
"It could be pretty big … if we find what we suspect (sic) we are looking for", one investigator said.
A police spokeswoman said the man had been arrested on "suspicion of involvement in the commission, preparation or instigation of acts of terrorism".
He was been taken to a police station in nearby Wiltshire.
Home Secretary David Blunkett said: "It is believed by the security and special branch services that this man has connections with the network of al-Qaida groups.
"We would not have taken these steps if we didn't believe that this individual posed a very real threat to the life and liberty of our country," he told local television.
Police said Thursday's operation was the culmination of months of investigation, but investigators declined to comment what police suspected the man was planning.
Officers were also searching two addresses in the northern town of Blackburn in connection with the arrest of the 24-year-old, who is believed to be a British-born Muslim.
A 39-year-old man was also arrested by police on Thursday in the northern city of Manchester, Scotland Yard said.
However the source said this arrest was unconnected to the operation in Gloucester.
Britain's most senior police officer Sir John Stevens said last week that London would be on high alert for the foreseeable future after previously warning that an attack on the UK was almost inevitable.
Earlier this month, security services were moved to a heightened state of alert after they received warnings of a possible attack by Usama bin Ladin's al-Qaida group, blamed for the 11 September 2001 attacks on the United States.