The problem with Prince Charles, heir to the British throne and now nearly 32 years old, is that he has still not married.

Like so many nagging mothers and maiden aunts, the British press will not let him alone until he does. Each new "girlfriend" seen with him in public rates a front-page picture in the tabloids; third-hand reports of who he might be meeting at a royal hideaway fill the gossip columns; and every speck of speculation about which lucky lady may become his bride and future queen becomes an affair of state.

It happened again last when the most persistent version of this speculation -- that the prince might marry Princess Marie-Astrid of Luxembourg, who is Catholic -- was revived by, of all people, one Thomas Orr, the grand master of the Grand Orange Order of Scotland, a bastion of old-fashioned Protestantism. He announced to reporters that he had recently been assured by a cabinet minister that British law would never be changed to allow Prince Charles to marry a Catholic and still succeed his mother, Queen Elizabeth II, on the throne.

The subject apparently had come up routinely in a discussion of sectarian problems involving the Protestant majority and Catholic minority in British-ruled Northern Ireland in a meeting between Orr and other Orange Lodge leaders and Britain's Northern Ireland secretary, Humphrey Atkins. In answer to a question, Atkins apparently said he knew of no government plans to alter the Act of Succession of 1701, which decrees that the throne can never be occupied by a Catholic or anyone who marries a Catholic.

Orr claimed this was a promise that the law would never be changed. When British bureaucrats said that was not exactly what Atkins had said, other prominent Protestant politicians, notably the Rev. Iain Paisley, the leading militant Protestant politician in Northern Ireland, jumped into the fray, demanding that Prime Minister Margaret Thatcher "make a clear statement" on the matter. Paisley predicted a constitutional crisis and chaos if an attempt were made to change the law, and especially if Prince Charles married a Catholic and did not give up his claim to the throne.

Thatcher repeated that her government had no plans to change the law and it remained in force. Buckingham Palace then took the unusual step of making a blunt statement denying that the prince intended to marry Princess Marie-Astrid or even knew her very well.

"There are no plans whatsoever for a marriage between the Prince of Wales and Princess Marie-Astrid of Luxembourg, and there never have been," a palace spokesman said. "There have been no meetings whatsoever between the Prince of Wales and Princess Marie-Astrid in recent years. Any suggestion to the contrary is totally without foundation."

Missing in all this was a single shred of evidence suggesting any friendship, romance, or arrangement to marry between the prince and the princess, beyond newspaper stories, following Orr's statement, that dredged up old press reports of the alleged courtship.

According to these accounts, the princess first met Prince Charles when she was a teen-ager, representing her parents, the Grand Duke and Duchess of Luxembourg, at his investiture as Prince of Wales and heir to the throne. oIt was his mother, the queen, who reportedly was later "enchanted" by the princess during a visit by the British royal family to Luxembourg.

She is believed to have arranged a lunch in Brussels near the end of 1976 attended by Prince Charles, Princess Marie-Astrid, other royal personages and, apparently most significantly, a Belgian cardinal and a representative of England. Buckingham Palace has repeatedly denied or refused to comment on this story.

In any event, it is supposed to have been leaked to the press by someone in the royal family, producing a June 1977 front page in the tabloid newspaper The Daily Express declaring: "Charles to Marry Astrid -- Offical."

That premature report, so the story goes, dashed the queen's hopes for marriage between Charles and Princess Marie-Astrid. Except for the problem of religion, this is a pity, according to British social reporters. One wrote this week that Princess Marie-Astrid "is exactly the kind of girl for whom Prince Charles apparently has a preference: slim, blonde, attractive and intelligent."

The glare of publicity also is believed to have wrecked Prince Charles' own hopes of marrying a properly Protestant and at least equally attractive British blueblood, Lady Jane Wellesley, daughter of the present Duke of Wellington, who was frightened off by the photographers who followed her everywhere after she began spending time with the prince.

Today, he is seen in public -- at polo matches and on holidays and the like -- with a great many different young women. One of them, Lady Sarah Spencer, a goddaughter of Queen Elizabeth's mother, described in a women's magzine a few years ago how the Prince's lady friends must call him "sir" and are driven around by him personally in his Astin Martin sports car. "

But the Princess Marie-Astrid affair, as far as the British public is concerned, is not yet over. Some Catholic Labor Party members of Parliament have introduced a bill that would, whether or not Charles wanted to marry Marie-Astrid, remove from the Act of Succession the prohibition against the heir to the throne's marrying a Catholic.

Because it is privately introduced, rather than a government bill, it has little chance of becoming law. But it will provide an opportunity for a brief debate and a straw vote on the issue in the House of Commons later this month.

The issue has also remained alive in the "notice board of the establishment," the letter column of The Times of London. A Scottish lawyer and "devout Anglican" noted the absurdity and rank discrimination in the fact that their heir to the throne is barred only from marrying a Catholic. "There is no legal impediment," wrote Ian Moncreiffe, "to a future sovereign's marriage with a Morman, nor even with a Hindu or a Moslem."

Another correspondent said the prince could take his case to the European court because the European convention of human rights prohibits countries in the Common Market from discriminating against anyone's right to marry on religious grounds.

The Times itself, known in headier days of the British Empire as "The Thunderer," rather meekly editorialized against perpetuation of religious prejudice in Britain. But it nevertheless expressed the hope that the Act of Succession would not be put to the test by Prince Charles.

Britain has been through that kind of trauma within living memory, as British television viewers were also reminded this week, when "Edward and Mrs. Simpson," the dramatic recounting of the abdication of Edward VIII to marry the divorced woman he loved, began a repeat showing here.