Britain's domestic Press Association news agency quoted unnamed sources as saying those detained were Libyan, while the BBC said it was believed the arrests related to the Libyan Islamic Fighting Group (LIFG).
Two offices belonging to the Sanabel Relief Agency (SRA) registered charity, one in Birmingham, west central England, and another in the northwestern city of Manchester, were among a number of properties raided.
Police confirmed that one of those arrested was 44-year-old Taher Nasuf.
Nasuf was named by the United States earlier this year as a "middle-ranking member of the LIFG", a group it said has links to the Al-Qaeda terror network.
Born in the Libyan capital Tripoli, he is said to be one of three trustees and a director of the SRA, whose mission statement is to "aid and relieve Muslims in the destitute parts of the world", according to its website.
The US State Department, which also named four other Libyans allegedly involved with the LIFG, claimed the SRA and three other British-based real estate agencies were "instruments used to funnel resources" to the proscribed group.
Searches continuing
Greater Manchester Police (GMP)'s Anti-Terrorist Unit co-ordinated the raids with help from a number of other police forces and Britain's domestic security agency MI5.
First reports said eight people were arrested, but police later updated this to nine. Two of those detained were later released before police announced a 10th person had been arrested in the Manchester area.
Of the eight still in custody, five have been detained under the
Immigration Act 1971, which gives the home secretary (interior minister) powers to deport foreign nationals whose presence in Britain is deemed "not conducive to the public good for reasons of national security".
The three others were being held under the Terrorism Act, police said.
GMP Chief Constable Michael Todd said there was no threat of an attack on Britain but the operation was focused on alleged overseas activity.
"We are not talking today about a direct threat to the UK. We are talking about the facilitation of terrorism overseas. That could include funding, providing support and encouragement to terrorists," he said.
"This is an intelligence-led operation. We have been gathering intelligence, together with our security service colleagues, for at least a year, looking at the funding and support of terrorist activities overseas."
Searches were continuing at addresses across the country: 12 in Greater Manchester, one in the nearby Liverpool area, one in Middlesbrough, northeast England, three in the West Midlands and one in London.
The US State Department statement on February 8 this year officially designated the LIFG as having Al-Qaeda links, stating it supported terrorist activities in Libya and had attempted to overthrow Libyan leader Muammar Gaddafi.
At the same time, the United Nations Security Council froze all assets belonging to the five named individuals, including Nasuf, and the companies.
A GMP spokeswoman refused to say whether any of the other four individuals named by the US were among those detained when contacted by AFP.