While the rush by American banks to open London offices may be over, and even as New York prepares to inaugurate an international banking facility later this year, there is little indication here that this traditional capital of world finance is on the wane.

Interviews with American bankers here confirm that this is still very much the place to be to conduct international banking, and several banks from the Washington region have joined the race for business in London.

The great push to enter this market occurred during the early 1970s. The reason was the growth of the Eurodollar market, now $600 billion net. In response to that influx and to the problems that came in the wake of the mid-seventies recession, the British Banking Act of 1979 -- the first in 125 years -- was passed. Its intent was to "clarify" the situation, but it had the effect of creating a two-tiered system of banks, and some U.S. banks were downgraded in status.

Despite the controls, Britain is still considered to have one of the most liberal banking systems in the world, far more so than the United States. There are now 342 foreign banks in London, most of them in the heart of the financial district. There are roughly 40 branches of American banks here, 15 major subsidiaries, such as merchant banks, and 18 representative offices. Although several have left recently, still others are reported to be eager to come.

Among Washington-region banks doing business in London are Riggs National, Maryland National, and First National of Maryland.

Unlike the giants, Riggs National Bank is housed in a historic town house on a narrow, winding lane off the main commercial thoroughfare. The first floor houses computer operations while the upper stories, with their antique-filled rooms, provide the setting for the gentlemanly business of international banking. Much of it is done in the private dining room on the top floor. The occasional Riggs customer from back home who manages to find the company logo is accommodated, but the bank does not promote retail operations.

Riggs, which has a staff of 18, opened its London office, categorized as a licensed deposit taker, in June 1980. In that short time it has already turned a profit, thanks in part to the management of William H. Ryland. A former chief of American Security Bank's international division, Ryland, 47, is a native of Baltimore. Henry A. Dudley Jr., in charge of credit policy, spent a number of years at the Export-Import Bank. They feel their "Washington connection" is an important marketing tool in this competitive environment.

Riggs came to London to follow its customers, which include many embassies, and also to chase petrodollars. The problem is not how to raise money, said Ryland, but how to make it turn a profit. The bank's international portfolio is primarily sovereign-risk loans, followed closely by bank risk loans. Just 10 percent are commercial loans.

Its London office follows that mix at present. It is quite active in the short-term debt market. Such loans are used by large corporations to pay down their more expensive long-term loans. The bank is also engaged in large, syndicated Eurodollar borrowing. And it looks for trade opportunities for export.

This is the start of the second stage of Riggs' London strategy (the first was to break even), a changing of the portfolio mix that Ryland estimates will take another two years. Although he concedes Riggs will never be a major competitor with the big American banks, he would like to assume a share of the business from multinational corporations. Riggs eyes the so-called club deals, $40-million-to-$50-million loans that are too small to interest the giants. These, he says, can be the lifeblood of regional banks in London.

Riggs' overseas operations had assets of $1 billion at the end of 1980, or 30 percent of the bank's total assets. While the different divisions are not broken out, London accounts for about 10 percent of the bank's total assets, according to Ryland.

Maryland National Bank is technically outside the city; its offices are in a modern, high-rise building just on the other side of the remains of the Roman wall that once marked London's boundary.

Although Marynat is now the largest bank holding company in the mid-Atlantic region, with assets of $4.4 billion, a decade ago it did not feel large enough to go it alone in Europe. So it became a charter shareholder in the London Interstate Bank along with the Indiana National Bank and, currently, Gotabanken, the third-largest private commercial bank in Sweden, and Sparekassen SDS, the largest savings bank in Denmark and Scandinavia. W. Griffin Morrel Jr., a Marynat senior vice president, is chairman of London Interstate, and Marynat President Alan P. Hoblitzell Jr. is a director.

London Interstate is a recognized bank with assets of 7.8 billion pounds sterling. It conducts full banking services in the United Kingdom and makes loans around the world, with about half of its lending activity concentrated in Britain and Western Europe. For the year ending March 31, 1981, it showed a net profit of 420,000 pounds. Marynat gets a 25 percent share of the profits "with little of the expense," according to Stephen Schock, who is Marynat's local liaison with London Interstate. The only time there is a conflict, he said, is when some of Marynat's best customers try to get interstate loans at less than the going rate.

Schock, 29, also serves as Marynat's representative in London. Back in 1973 the home office decided it wanted more name recognition here, so it established a representative office as financier to the growing export trade out of the port of Baltimore. For a while it was a two-man operation, but later it was cut back to one and a secretary when not enough business was generated.

Schock, who started as a Marynat management trainee in 1974, spends between a third and a half of his time calling on Maryland customers with international business and European clients who do business in the mid-Atlantic region. Some of these are Black & Decker, McCormick & Co., PHH Group Inc., Associated Engineering and British Aerospace. His responsibilities include Scandinavia as well as the United Kingdom. The actual loans are made by the home office.

Marynat also has offices in Singapore, Mexico, Brazil and Nassau. Its international division assets average between 10 percent and 15 percent of the bank's total assets. Of that 10 to 15 percent, about a third is generated by its European group. The same is true for profits.

The First National Bank of Maryland also has headquarters in the city. It is in a three-story, 18th century building that used to be a wine shop. Flower-filled window boxes on the balcony and greenery on the square in front hark back to the days when the city was indeed a "financial village."

First Maryland, which came to England in 1978, is a licensed deposit taker. It is headed by Richard H. White, vice president and general manager. According to American colleagues here, the bank enjoys an excellent reputation in the banking community. The home office in Baltimore refused The Washington Post's request for an interview with White unless written questions were submitted in advance.

American banks in London employ some 9,500 people, most of them British. The number of expatriate American bankers here is somewhere between 500 and 1,000, according to the American Bankers Association in London (ABAL). And though their numbers are not growing significantly, their business is. In the United Kingdom alone, ABAL estimates American banks have a 15 percent share of total corporate lending, amounting to about $16.7 billion.

American banks, like other foreigners, are primarily engaged in foreign exchange and wholesale banking services offered to multinational corporations. They are not, as a whole, involved in retail banking, although there are some notable exceptions such as Citibank. Due to the European recession, the intense competition here, and the high cost of doing business -- office space rents for twice the Washington rate -- some banks are said to be anxious to expand retail operations, particularly home mortgages.

Today the size of American banks' sterling portfolios is increasing while their dollar portfolios are decreasing. "In essence, we're becoming local banks because the dollar is a less dominant currency," said Frank R. Reilly III, vice president and general manager of U.K. operations for Chase Manhattan. There are even rumors of takeover attempts on British banks by American banks. But Reilly says that apart from the fact there is little to acquire, "the Bank of England would have strong feelings if anybody came over and took over a significant portion of the local sector." And the Bank of England's "strong feelings" are tantamount to law in Britain.