A letter-bomb campaign against prominent Britons, responsibility for which has been claimed by the Provisional Irish Republican Army, has apparently failed.

At least a dozen such bombs, disguised as small Christmas packages in gold, green and brown wrapping, were mailed from Brussels during the past week. The covering envelopes were addressed by hand to British executives and politicians.

Three of the mail bombs exploded in postal sorting rooms in Belgium and Britain, causing only a single injury. The rest have been spotted by alert British and Belgian postal workers or intended victims. These bombs were safely defused by police explosives experts.

Among the targets were Employment Secretary James Prior, British Steel Chairman Sir Charles Villiers, Courtaulds Ltd. Chairman Sir Arthur Knight, British Institute of Directors Chairman Sir William Mather and former civil service chief Lord Crohan.

The Provisional Irish Republican Army has claimed responsibility for the mail bombs in a telephone call to the BBC office in Dublin, Ireland. The caller said they were intended for "members of the establishment" to highlight the continuing political protest by convicted IRA terrorists in the Maze prison in British-ruled Northern Ireland. The convicts claim political-prisoner status for their effort to join largely Protestant Ulster with predominatly Catholic Ireland.

A total of 110 persons including 38 British soldiers and nine Ulster prison officers have been killed in sectarian violence in Northern Ireland this year. The toll for members of the security forces there is the highest since 1973, demonstrating the relative success of a reorganization of the Provisional IRA into smaller cells.

Today, Prime Minister Margaret Thatcher made her second surprise trip to Ulster to visit British troops and Ulster police and prision officers and discuss security problems with officials. Accepting token Christmas gifts and donning a parachute regiment's red beret, Thatcher told the security forces, "I came because I wanted to see you and wish you a happy, and more important, a peaceful Christmas and New Year."

British police theorize that IRA agents in Belgium sent the bombs to names and addresses selected from a who's who that may be a year or two out of date. The bomb intended for Lord Croham, for example, was addressed to him as Sir Douglas Allen, his name before becoming a peer, at a home he last lived in a year ago.

The bomb mailed to Mather, however, reached his country home in Cheshire. After reading about letter bombs intercepted earlier, he suspicious of the unexpected package and put it out in his yard before calling police.

Lady Villiers did the same thing with a diguised mail bomb addressed to her husband, the British Steel chairman, even though she is a wartime refugee from Belgium with friends there.Because the handwriting on the the package was unfamiliar, she said, "I knew immediately that there was something odd. I thought there was a fair chance that it was a bomb because of all the publicity."

Scotland Yard has sent antiterrorist investigators to work with Belgian police in Brussels, where earlier this year a man mistaken for a British diplomat was murdered and a bandstand was blown up just before a visiting British military band was to give a concert. The Provisional IRA is suspected of being behind both of those attacks.

This year's IRA holiday terror campaign against the British occupation of Northern Ireland began during rush hour on Nov. 26, when 20 bombs were detonated in cities, towns and trains through Ulster, injuring 13 people. w

On Dec. 26, five British soldiers were killed when two antiterrorist patrols in Ulster were ambushed by remote-control bombs near the Irish border. The next day, an Ulster prison officer was shot to death on the street near a jail in Belfast.

Thatcher made her first visit to troops in Ulster shortly after British Lord Mountbatten, members of his family, an employe and 18 British soldiers were killed in coorinated bomb attacks on both sides of the Ulster Irish border in August.

Today's trip, like the last one, was arranged in secret and took Thatcher to dangerous posts along the border. She returned later to the prime minister's country estate at Chequers to celebrate Christmas with her family. m