Britain and Ireland took a significant step this week toward establishing closer relations with each other and improving the climate for dealing with the problem of sectarian strife in British-ruled Northern Ireland.

Because of the political sensitivity of the talks for both countries, widely differing official interpretations have emerged from Monday's Dublin summit between prime ministers Margaret Thatcher of Britain and Charles Haughey of Ireland. But well-informed officials here and in Dublin agreed that it marked an important shift in the often strained relations between the two countries since all but the six northwestern counties of Ireland won independence from Britain a half century ago.

Most importantly, it offers the potential for closer cooperation, if not yet a joint approach, to the politcal problem of Northern Ireland, where the Roman Catholic minority seeks reunification with Ireland, and the Protestant majority wants to remain part of Britain.

"We are ironing out old misunderstandings and opening up regular avenues for discussion of all the issues that concern our two countries," an Irish official said. "We now have a framework for mutual discussion that has been lacking between us."

According to British officials, one result of the summit was that Thatcher gained Haughey's support for her handling of a hunger strike by imprisoned terrorists of the Irish Republican Army's Provisional Wing.

Although Haughey was best known for his strident nationalism when he became Irish prime minister a year ago, his has greatly strengthened security measures against Irish nationalist terrorists carrying on a campaign of bombings and shootings in Northern Ireland.

In return for Haughey's support on the strike, Britain appears to be giving Haughey the opportunity he has sought for a potentially larger Irish role in deliberations about the political future of Northern Ireland. But British officials reiterated that it must remain part of Britain until and unless a majority of its residents and the British Parliament decide otherwise.

However, Irish officials also said that further talks could eventually lead to a joint Anglo-Irish approach to the problem of Northern Ireland. In their communique after the summit, Thatcher and Haughey agreed that the "economic, social and political interests of the peoples of the United Kingdom of Great Britain and Northern Ireland and the Republic [of Ireland] are inextricably linked, but that the full development of these links has been put under strain by the division and dissent in Northern Ireland."

To "achieve peace, reconciliation and stability," the communique declared, "a further development of the unique relationship between the two countries" is required.

Haughey, who called the summit agreement an "historic breakthough" in Anglo-Irish relations, hinted that this could lead to some kind of confederation or new political arrangement between Britain and Ireland, which has stirred Irish hopes of eventual unification with Northern Ireland. w

"For the first time we have a regular institutionalized role in discussing Northern Ireland," said one Irish official. "To us, the totality of relationships in these islands includes Northern Ireland."

But british officials, concerned about an already building backlash by political leaders of the Protestant majority in Northern Ireland, played down the communique's references to the British-ruled province.

"We have always thought Ireland had an interest in what happens in Northern Ireland," said one British official, "and have only put into words what already is."

"We knew [Haughey] would talk about confederation and get political capital out of this," the British official said. "but the future of Northern Ireland will be decided in London and he knows it."

British officials added, however, that Thatcher is impressed by Haughey's growing political strength at home and his support for strong security measures against Irish nationalist terrorists.

In addition, a British official said, "Mrs. Thatcher needed Mr. Haughley's support on her handling of the hunger strike and she got it. We are all trying to keep ahead of the IRA propaganda campaign surrounding the strike."

Seven IRA Provisional Wing terrorists convicted of crimes including murder, attempted murder and armed robbery have refused to eat for 50 days, and three are believed to be near death. The Britsh government fears a wave of Christmas season IRA bombings in Northern Ireland and here in London if any of them do die. All police leaves were cancelled in Belfast today.

The seven men have been joined in their hunger strike by three women IRA prisoners and six convicted Protestant terrorists, all of them also demanding special status as political prisoners for hundreds of convicted Catholic and Protestants terrorists in Northern Ireland's prisons.

British officials reiterated this week that they will never grant political status for prisoners convicted of crimes such as murder and robbery, but they also made clear they are ready to negotiate on prison conditions for all convicts in Northern Ireland.