A group of private investors, backed by the British banking firm of N.M. Rothschild and Sons, is offering up to $1 billion to buy National and Dulles International airports from the federal government.

"We would have no trouble raising a great deal of money," said John Redwood, head of the bank's international privatization operations, and an active participant in the British government's efforts to sell many of its assets to the private sector. "The question is, 'Will the lawmakers in America allow the market to be tested?' "

That question comes as the Senate is debating a bill that would shift control of the two Virginia airports from the federal government to a regional authority for $47 million. Several senators have said they think the price is far too low, but any bid to run the airports for a profit would cause a tough political battle.

Transportation officials say that although no law would prohibit private ownership of airports, it would create vast regulatory problems.

"There is a history of running airports as service centers in this country," said Gregory Wolfe, a Department of Transportation official who is actively involved in airport issues. "To make that kind of change is not politically feasible here."

Major airports in the United States are owned by regional or municipal authorities and run as nonprofit enterprises, but the Reagan administration has been encouraging the private sector to get involved in businesses -- such as public transportation -- that once were run solely by government.

The Reagan administration originally considered selling the two airports to the highest bidder, but dropped the idea after a commission headed by former Virginia governor A. Linwood Holton Jr. proposed that a regional authority take control of them.

The Services Group Inc., an American consortium of economists and investors interested in privatization, say that Dulles and National, if run like a strict business, easily would make enough money to pay for themselves.

"Heck, I'll buy them myself for $300 million if they let me use the land any way I want," said Holton, who has spent much of this week lobbying Congress on the transfer bill before the Senate. "You could build apartments along the Potomac River and make millions. But we believe these things ought to operate as airports."

The bill before the Senate requires the regional authority to reinvest any profits from the airport.

The transfer bill has run into trouble on the floor of the Senate, where Sen. Paul Sarbanes (D-Md.) has spent the last two days filibustering to stop it. Maryland officials have objected to the transfer, saying that the price is too low and that it would place Baltimore-Washington International Airport, which the state owns, at a competitive disadvantage.

Both National and Dulles need major capital improvements, and the federal government has been unwilling to make significant investments in either airport for years. A new owner -- private or public -- would have to pump as much as $500 million into them almost immediately.

Redwood, who has been involved in the United Kingdom's attempt to privatize its airports, said that in addition to increased landing fees -- which many aviation experts view as inevitable at National and Dulles -- money could be raised by selling shares of the corporation that owns the airports.

He said that if he gets a sense from Congress that it is willing to look at privatization he would begin to assemble a group of investors willing to buy the airports.