The immigration official at London's Heathrow Airport glanced at the government officials' passport of Alfred E. Eckes Jr., the chairman of the International Trade Commission, and asked if he was with the FBI.

Eckes, a mild-mannered economic historian and former Republican congressional aide, replied that he worked for the ITC, an agency hardly as well known as the FBI.

"That's nearly as bad," said the British immigration officer. "You really stuck it to us on steel."

A few years ago it would have been unlikely that many Americans, much less a British immigration official, would have heard of the ITC.

Six years ago, recalls public information officer Hal Sundstrom, it did not even have a PR person -- an unheard of thing for a Washington agency.

But the ITC has made more headlines during the past year as recession-hit American industries have flooded it with complaints that foreign competitors had violated international trade agreements by dumping products here at below-market prices or receiving subsidies from their governments.

Now foreign governments and industries pay close attention to the agency.

The announcement of the commission's preliminary finding in a complaint involving $1.7 billion worth of Canadian lumber imports, for instance, drew TV coverage by the Canadian Broadcasting Corp.

The ITC is now involved in dozens of other cases that are causing friction between the United States and its trading partners.

Today it is holding a hearing on a request by Harley-Davidson to protect it from Japanese motorcycle imports.

On Wednesday the commission will take up another prickly issue for the European Community -- a request to end duties on dairy products from the Common Market. The Reagan administration has threatened to dump surplus American butter and cheese on world markets if the Europeans continue to subsidize their farmers.

Despite all this new publicity, its staff remains small -- 413 persons, including 265 analysts -- squeezed into one of those Greco-Roman buildings tucked into a block of E Street NW.

In 1931, as the United States Tariff Commission, it had 390 employes, showing what must be one of the slowest growth rates among federal agencies.

Its analysts are famous for the breadth of their knowledge. The ITC phone book, for instance, lists experts in almost any industry the ITC could be called on to investigate, from abaca (a textile product) to zoris. Its experts watch 12,000 items of world trade.

But while business is booming, the number of commissioners has dropped from a full complement of six to just three, which under the Government in the Sunshine law means no two of them can ever get together casually since that would constitute a quorum for an official meeting.

Two new members have been nominated by President Reagan and Eckes hopes they will be confirmed during Congress' lame-duck session so he can begin talking again when he meets a fellow commissioner in an elevator.