Prime Minister Margaret Thatcher admitted to reporters at a press conference at this summer's British Commonwealth conference in Lusaka, Zambia, that "I sometimes have a way of saying things I shouldn't say."

"Hear, hear," piped up a British voice in the background, causing nervous laughter. The voice was that of Thatcher's foreign secretary, Lord Carrington.

Earlier in Lusaka, according to a story making the rounds of government offices in Whitehall here, when Carrington handed Thatcher the final copy of the speech signaling her dramatic shift in policy on the Zimbabwe-Rhodesia problem, he was overheard sternly instructing her to stick to every word of the prepared text with none of her extemporaneous embellishments.

These two incidents -- one recorded on tape by reporters at the press conference and the other possibly apocryphal but widely believed -- illustrate both the two sides of Carrington's personality and the important dual role he plays in Thatcher's Conservative government.

Beginning this week, Carrington moves from behind the scenes into the spotlight as the star of perhaps the most important foreign policy drama of Thatcher's administration -- the constitutional conference for Zimbabwe-Rhodesia.

As conference chairman and its opening speaker, Carrington is setting the agenda and stage-managing the deliberations by the delegations from Britain the Muzorewa government in Salisbury and the Patriotic Front guerrillas fighting from within Zimbabwe-Rhodesia and neighboring Black African nations.

Carrington, short, spectacled, sharpnosed and almost elfin in appearance, displays an impish, yet suave charm that disarms almost everyone he meets and frequently diffuses the tension of government and diplomacy, When Thatcher becomes noticeably annoyed with colleagues in her cabinet according to one knowledgeable source, Carrington draws off her anger by playing the court jester, needling her and then often making himself the butt of the joke.

But Carrington also has a tough, supremely self-confident side and pushes hard for what he wants. He has been credited with almost single-handedly turning Thatcher around on Zimbabwe-Rhodesia and on the admission of more Vietnamese refugees into Britain, He also played an important role in shaping her response to the terrorist murders of Lord Mountbatten and 18 British soldiers in Ireland and Ulster two weeks ago.

By all accounts, Carrington is one of the two most important figures in Thatcher's government. The other is the bulky, bulldog-like Home Secretary William Whitelaw, who also hides with self-deprecating humor an assurance born of long political experience that often makes his last word heard in a Cabinet discussion before Thatcher makes decisions. Whitelaw is most influential in domestic policy, Thatcher's chief interest when she became prime minister in May, while Carrington shapes foreign policy, in which Thatcher had relatively little previous experience or interest,

Born in 1919, Peter Alexander Carington (his family name contains one less "r" than his titled name because of an 18th century heraldic error) became the sixth Lord Carrington and owner of 800 acres of Buckinghamshire countryside and villages on the death of his father in 1938. After military service during World War II, he plunged into politics in the House of Lords, in which he has a lifelong seat.

His unusual energy in that predominantly gerontic body earned him at an early age a series of Conservative leadership positions.

An important figure in what must be considered a right-wing government, Carrington is suspected by Britain's most doctrinaire conservatives of being a closet liberal, an anachronistic whig who may be conservative in principle but untrustworthily pliable in action;

Carrington, in fact, speaks of himself as being "pragmatic" and has said that "this seems to be the essence of being Conservative. You adapt to the circumstances around you."

Although he and Thatcher have crushed for the moment an incipient right-wing Conservative Party revolt against the Zimbabwe-Rhodesia initiative and the offer of refuge here to more Vietnamese refuges, Carrington's conduct of the constitutional conference here will be watched closely and could become a chief topic of debate at next month's annual Conservative Party conference.