According to rampant media speculation here, bolstered by discreet signals from Buckingham Palace, Prince Andrew, the second son of Queen Elizabeth and fourth in line for the British throne, is engaged to be married.

The engagement between Andrew, 26, and Sarah Ferguson, also 26, reportedly was agreed to over the weekend but an official announcement was being withheld to avoid stealing publicity from Prime Minister Margaret Thatcher's new budget, due today. While the palace maintained a benign silence, however, television equipment was being moved inside for an undisclosed announcement set for 11 a.m. Wednesday. Indications were that the betrothed couple would be interviewed for national broadcast.

Widespread reports said the wedding would take place next fall at Westminster Abbey. As a social and historical event, it would fall considerably below the 1981 ceremony joining Andrew's elder brother, Charles, with Diana Spencer at St. Paul's Cathedral.

Only twice during the Windsor family reign have second sons ascended to the throne, one replacing his brother, an heir who died without issue, and another replacing a brother who abdicated. Charles, in line to take over from his mother as monarch, already has two sons who outrank Andrew.

But Andrew, who is considered more handsome than Charles and more congenial than his sister Anne, has a special place in the heart of the British. Although not known as a deep thinker, he is a dashing naval officer whose heroic exploits as a helicopter pilot during the 1982 Falklands War with Argentina were well chronicled here.

Andrew's romantic escapades have been even more closely followed. Nicknamed "Randy Andy" by the tabloid press, he has been linked over the past several years with a number of women. Most, however, have been aspiring movie starlets or fashion models considered unsuitable as royal consorts. Chief among them was Koo Stark, an American-born actress whose career history included nude appearances in a series of films and published photographs that caused considerable controversy during her nearly two-year relationship with the prince.

No such skeletons are likely to appear from Ferguson's closet. Like her good friend Princess Diana, who reportedly promoted the romance, Ferguson has a few drops of royal blood. Her father, Maj. Ronnie Ferguson, who serves as Prince Charles' polo manager, is a first cousin of Princess Alice, Duchess of Gloucester, widow of the queen's uncle.

Like Diana, Ferguson comes from a broken home. The fact that her mother, Susan Barrantes, left her father to marry a professional polo player from Argentina -- with which Britain still maintains a formal state of hostility -- is not thought to count too heavily against her.

Nor is Ferguson's now widely publicized three-year romantic liaison with a man 22 years her senior likely to stand in the way. According to press reports, that tie ended early last summer when she told Paddy McNally, a racing car consultant, to marry her or they were through. Shortly thereafter, she made her first public appearance with Andrew in the royal box at Ascot.

As the Sunday Times noted last weekend in reference to similar curiosity displayed and satisfied at the time of Diana's betrothal, "Two virgin princesses in one generation is more than even the royal family can reasonably expect."

The British press, having satisfied itself that Ferguson has no unacceptably dark past, has concentrated in recent days on her physical attributes. They include a ready smile, flaming red hair, and what The Sun, Britain's largest circulation daily, has pointed out is "much more in the melons department than skinny Koo Stark and the other slender showgirls."

Ferguson, a director at a graphic arts company, describes herself as a "working girl," but appears to have had ample free time available in recent months for royal-related outings, including visits to Andrew's ship and a Swiss skiing vacation this winter with Charles and Diana.

Like Diana, she is often described as a Sloane Ranger, current trendy shorthand for the young generation of upper-middle-class Londoners whose social and shopping lives center around Sloane Square in London's fashionable Chelsea district. More preppy than yuppy, Sloanes are generally straight and well dressed, and considered somewhat frivolous.

Ferguson shares a two-bedroom apartment with another woman in Clapham, in south London. If the engagement is on, however, she is likely to move into Buckingham Palace or some other royal residence for protection and privacy until the wedding. Although she is known to be adept at avoiding the press, speeding through London traffic in her blue BMW, the pressure is likely to increase measurably.

Since last weekend, dozens of reporters and photographers have been camped out on her doorstep, waiting for her to emerge in the morning and following her every move. Several minor casualties were reported today as cameramen, walking backwards in front of her in a group, fell into a construction site trash heap. As Ferguson walked about 200 yards this afternoon from her office to a nearby hotel, a small motorcycle was pushed over into a crowd of pedestrians, and a woman bystander selling charity stickers reportedly was nearly crushed into an adjacent railing.