The Queen was still planning to attend Remembrance Sunday celebrations at the Cenotaph in central London later today amid "unprecedented security".
Despite fears for her safety, she was determined to lead the nation's tribute and lay the first wreath, sources said.
Computers and documents seized from suspects' homes and were being examined.
Scotland Yard said: "These arrests and searches are part of an ongoing investigation into Islamist-related terrorism.
"Officers from the Metropolitan Police Service's Counter Terrorism Command (SO15) are working closely with colleagues in the SE Counter Terrorism Unit and MI5." None of those arrested were believed to have direct links to Syria, but were suspected of being jihadists.
As well as the four arrests, a number of residential addresses and vehicles, in Greenford, Hounslow, Brentford and Walthamstow were searched.
The arrests and searches were part of an "ongoing investigation into Islamist related terrorism", police said.
In August, Home Secretary Theresa May raised Britain's terrorism threat level from "substantial" to "severe" - the second-highest of five possible threat levels - because of the danger posed by Islamic State (Isis) and al-Qaeda sympathisers.
This is not the first time the Queen's life has been threatened.
The Lithgow Plot was an assassination attempt on the Queen and Prince Philip during a royal tour in Australia in 1970.
Their train struck a large log that was allegedly placed on the tracks, but the train was travelling slowly, averting any crisis.
In 1981, 17-year-old Marcus Serjeant was jailed for five years after firing six blanks at the Queen before the Trooping the Colour ceremony. In 1982, Michael Fagan, 31, broke into Buckingham Palace and entered the Queen's bedroom. He was not charged with trespassing but spent the next six months in a psychiatric hospital.