The man was detained on Wednesday after passing through a security check in the latest alert at a major international airport.
Police originally arrested the man, 45, for firearm offences but then said they were holding him under section 41 of the anti-terror law. It refers to the "alleged involvement in the commission, preparation or instigation of acts of terrorism".
"A quantity of suspected ammunition was found in his possession. The items are being forensically examined," said a statement from London's Scotland Yard police.
Heathrow security sources said the man had five bullets of two different types.
Security has been especially tight at Heathrow and other big world airports in recent weeks, with US-bound flights from Britain, France and Mexico grounded amid fears of a plot to carry out another September 11-style attack.
Spotlight on Dulles
With the US administration eager to see security beefed up at other airports round the world, Wednesday's incident raised the question of how the man got past security checks at Dulles airport in Washington.
BAA, Britain's biggest airport operator, confirmed the arrest and said Heathrow security staff had found "prohibited items" with the Sudanese man.
There are more security checks
for travellers since 9/11 attacks
Neither BAA, Virgin nor police would give more details of what the man was carrying.
"The safety and welfare of our passengers and crew is Virgin Atlantic's top priority," the airline said in a statement.
"The item seized did not pose a threat to our aircraft. Screening of passengers at Washington Dulles airport is the responsibility of the Transportation Security Administration."
The incident comes at a jittery time for the airline industry, with a string of flight cancellations and delays hitting Heathrow particularly badly.
Washington is demanding that airlines carry armed marshals on some planes, and has begun fingerprinting and photographing foreigners at more than 100 airports.
The incident comes at a jittery time for the airline industry, with a string of flight cancellations and delays hitting Heathrow particularly.
The United States is demanding that airlines carry armed marshals on some planes and has begun fingerprinting and photographing foreigners at more than 100 airports.
"We have always said that what matters most is security on the ground and that's where the government should be investing," said Jim McAuslan, general secretary of the British Airline Pilots' Association.
"We should not be led into a cul-de-sac of sky marshals."