Officers from the Metropolitan Police Service's Counter Terrorism Command (SO15) are searching 18 premises across the city and one property in Stoke-on-Trent in the West Midlands region of England.
The Met said the operation was part of an ongoing inquiry into Islamist-related terrorism and not in response to any immediate threat to the public. London-based preacher Anjem Choudary was among the arrested men, aged between 22 and 51, BBC reported.
They are being held "on suspicion of being a member of a proscribed organisation, supporting a proscribed organisation contrary to Section 11 and 12 of the Terrorism Act 2000 and encouraging terrorism contrary to Section 1 of the Terrorism Act 2006," a Met statement said.
The banned organisation is believed to be Al Muhajiroun, set up alongside Choudary by Omar Bakri Muhammad, who was told he could not return from Lebanon to the UK after the 7/7 bombings.
Police said a number of residential, business and community premises are being searched; 11 in east London, one in west London, one in north-west London and five in south London.
Britain last month raised its international threat level to the second-highest level of "severe", meaning an attack is considered highly likely, while Prime Minister David Cameron has said the Islamic State militant group in Syria and Iraq poses the country's greatest ever security risk.
The UK has recalled Parliament on Friday to take a decision on joining US air strikes against IS.