IT IS EASY to understand why British Prime Minister Margaret Thatcher might be exasperated by the problems of Northern Ireland. Not only does the violence affect thousands there and spill over in attacks on English soil, but Mrs. Thatcher herself, and many members of her government, have been the personal targets of terrorists. It is only weeks since she survived an attempt on her life at Brighton, and the loss of friends and colleagues in that bombing must be fresh in her memory.

Nevertheless, it is unfortunate that last weekend's meeting with Irish Prime Minister Garrett FitzGerald was later undermined by Mrs. Thatcher's brusque and dismissing comments during the following days. The long-planned summit was to have been an opportunity for both government leaders to discuss the problems of Ulster. Last March the New Ireland Forum, an organization of Dublin leaders and nonviolent Catholic parties in the north, produced a report detailing the scope of the problem, rejecting violence and offering a series of alternative steps toward cooperation among the three governments involved. The report was really a talking paper, and hardly anyone expected the British, in the near future, to adopt any of the constitutional reforms suggested. Even the authors of the report solicited responses, counterproposals and new ideas. The problems of Northern Ireland, after all, cannot be solved in a stroke, but must be managed cooperatively and attacked step by step.

At the end of the bilateral conference a carefully worded communiqu,e was issued announcing no breakthroughs, but heralding a few minor agreements. Both parties stressed it was in their interest to encourage peace and stability in Ulster. Both acknowledged that the rights and traditions of both Catholics and Protestants in the north must be preserved and that any change in the constitutional status of the province could be made only with the consent of a majority of the people living there. Another summit is scheduled for early next year.

After this bland but somewhat encouraging message was issued though, Mrs. Thatcher held a press conference and later answered questions in Parliament. In these exchanges she questioned the statement that there is an alienated minority in Northern Ireland, abruptly rejected a series of changes suggested by Dublin last March -- "That's out!" she said after each proposal was raised -- and suggested that the people of Northern Ireland could handle their problems without outside help.

Mrs. Thatcher and Dr. FitzGerald have a common enemy: the IRA. The terrorists can only find comfort in the prospect of failure for the cooperative efforts of London and Dublin, because continued violence and unrest is in the interest of the gunmen. His political enemies are already urging Mr. FitzGerald to abandon hope for a peaceful and cooperative settlement in the north. If that happens and the painstaking, slow process of accommodation is halted, the British, the Irish and most of all the beleaguered people of Ulster will pay the price.