By all appearances, Robert Allison Hill seemed to hold a place among the rich and well-bred of Washington society. Hill said he was the grandson of a railroad tycoon. He said he owned a castle in Tangiers and an investment bank in London, that he traded in gold and regularly played polo with Great Britain's Prince Philip.

Yesterday, Hill 46 pleaded guilty in U.S. District Court to one count of mail fraud. A federal prosecutor said Hill had used his tales of fabulous wealth to swindle a Washington couple out of $34,000, which he used to pay his own bills.

In exchange for the guilty plea, the government has agreed to dismiss 11 other fraud charges against Hill and 10 mail fraud charges against his wife, Annmarie.

Meanwhile, the Washington couple, Retired Adm. Walter Innis and his wife, Pauline, an author, have filed a lawsuit in D.C. Superior Court to try to recover the money they turned over to Hill. They lost it in a series of deals consummated at elegant restaurants, the Army Navy Club and on the steps of the Folger Theatre.

Pauline Innis said yesterday that she first met Annamarie Hill at the 1976 Washington International Horse Show. Hill, a cochairman of the event, pulled Innis' name out of a hat in a drawing for a bracelet.

The Innises, who live at the Watergate, assumed that the Hills, who lived at the Shoreham West apartments, were wealthy. They had a car and driver, went to exclusive clubs and expensive restaurants and had box seats at the symphony, Pauline Innis said. "We thought they must have money to live like that," she said in a telephone interview.

According to court records, this is what happened:

In July 1977, during a lunch at the Jockey Club, Robert Hill told Walter Innis that his London bank, called "Rothemoss," had overbought some British Petroleum stock. He offered Innis 2,000 shares at $4 below the market price per share of $16. There were further discussions at the Kennedy Center and then at the Army Navy Club, where Innis gave Hill a cashier's check for $24,000 to cover the stock purchase.

That November, at the Prime Rib restaurant, Innis, who had taken out various loans to buy the stock, asked Hill why he hadn't received any dividends. Hill suggested that the delays were caused by problems in currency exchanges and proposed that Innis invest another $10,000 in gold -- with a monthly $1,000 return to cover his outstanding loans.

After further discussions at the Sulgrave Club, Innis later met Hill on the steps of the Folger Theatre, where he turned over a check for $10,000.

Rothemoss, which Hill had set up, was dissolved by the Registrar of Companies in England months before Hill began the transactions with the Innises. The $34,000 was used by Hill for personal expenses.

In April 1978, after the Innises had seen neither their stock nor their income from the gold trade, they complained to the District police, the government said.

The Hills now live in New York City. Robert Hill, who faces up to five years in jail and a $1,000 fine on the small fraud charge, will be sentenced on April 3.