The Commonwealth agreement on a Zimbabwe-Rhodesian settlement plan this week provides an object-lesson in taking a small amount of common ground and building it into a new hope for peace.

Yet, despite the criticism that has already begun, the odds are strong that British Prime Minister Margaret Thatcher will bring the contending sides together next month, and there is even a reasonable possibility that some progress toward solving the seemingly intractable Zimbabwe-Rhodesian problem may be made.

There is virtually universal agreement that this will be the last diplomatic effort to settle the issue. Failure most likely will mean a major escalation of the war, increased flight among the 250,000 white minority and the potential for significant East-West involvement.

What the Commonwealth conference of Britain and its former colonies achieved was an agreement at the most basic level: For the breakaway colony to achieve legal independence it should have a new constitution approved by the contending parties followed by an election supervised by the British.

The agreement, if carried out, would mean that Britain would resume responsibility for Zimbabwe-Rhodesia for the first time since the colony illegally broke away in 1965.

The 41-member organization agreed not to wrestle publicly with the long-time problems that so far have defied solution: achieving a cease-fire in the six-year-old guerrilla war, disposing of the opposing military forces and supervising fair elections when the country is virtually an armed camp.

The agreement involves only two of the four key parties in the 15-year-old dispute: Britain, the colonial power, and the front-line African states - Tanzania, Zambia, Mozambique, Angola and Botswana - that support the Patriotic Front guerrilla war effort.

Left out of the bargaining so far are the two most difficult elements to bring together, the new Zimbabwe-Rhodesian government of Bishop Abel Muzorewa and the guerrillas opposing it.

Criticism of the Commonwealth agreement already has been heard from both sides, but much of this can be regarded as opening round skirmishing to establish the best position at the conference the British are expected to call next month.

One reason for possible success is that the situation has reached the stage of diplomacy of desperation. No nation has moved to recognize Muzorewa; the war continues space with upward of 500 each week, according to Thatcher, and 1,000 or more whites still flee the country each month.

More important for the chances of success, however, are the changes that have occurred since the Anglo-American negotiations, the last serious peace effort, bogged down last year.

Britain has a new Conservative government. A new black government is in Salisbury, although it is severly limited by white authority. Tanzania has been financially and militarily drained by its war in Uganda. Zambia's support for the guerrilla faction located on its soil has come into question under the pressure of numerous Rhodesian raids into the country.

The weakening on the African side may lead to pressure by the front-line states on the guerrillas to engage in meaningful bargaining at the conference table.

Ironically, the election of the Conservatives in Britain long hoped for by whites in Zimbabwe-Rhodesia as their potential salvation may turn out to be cruel blow to their hopes for maintaining their privileged position.

During her spring election campaign, Thatcher seemed determined to lift economic sanctions and recognize the new government quickly.

Now, after just three months in office, she had done a turnabout under the pressure of united African opposition to the Muzorewa government. She denounced the constitution negotiated by former prime minister Ian Smith and called for new elections, thus abandoning her previous strong leanings toward the Muzorewa government.

So, Smith's hope that the Conservatives would push to accept the government he helped to create has now disappeared, barring a party revolt against Thatcher. He has nothing better to hope for from the British political scene.

The Rhodesia Herald newspaper, which generally reflects white opinion, asked half in sorrow, half in mirth if Thatcher was not perhaps a Labor prime minister "in drag."

The British move also takes President Carter off the hook at least for a while. Congressional pressure for him to lift sanctions and recognize Zimbabwe-Rhodesia should ease at least while Britain is in the midst of its new diplomatic effort.

Salisbury had been banking on a lifting of sanctions. One white official there said recently, "It's not a question of whether sanctions will be lifted but simply how and when."

The Africans applied a very successful carrot-and-stick approach in bringing about Thatcher's change in position. First, they united behind the Patriotic Front at the Organization of African Unity summit last month in Liberia, naming it the "sole legitimate representative" of the people of Zimbabwe, the African name for Rhodesia.

Then the five front-line states held a rare summit of all their leaders who days before the Commonwealth conference to coordinate policy behind the leadership of Tanzanian President Julius Nyerere. Instead of criticizing Britain, however, Nyerere spoke hopefully about the possibility of cooperation.

Oil-rich Nigeria then applied the stick and announced plans to nationalize British Petroleum's $150 million interests in the country. Britain railed against the move, saying it was counterproductive. In the end, however, Thatcher agreed that there had to be a new constitution and new elections for Zimbabwe-Rhodesia to achieve legitimacy.

The British, worried about right-wing Conservative opinion at home, maintained that there was no change, just a "progressive revelation of policy." The Africans were willing to go along with that publicly, thus helping to protect Thatcher on her home front. The Commonwealth, in fact, provided the umbrella for her to complete the change in a multilateral arena.

Thatcher, however, comes into the expected negotiations with considerable weapons. Whites in Zimbabwe-Rhodesia, although they may be disillusioned, know they will get no more favorable British government to deal with.

The Africans, aside from their own domestic problems, know that Thatcher's original inclinations were to lift sanctions, and they must realize that she may still do so if all else fails.

Indeed, Thatcher may have another option. She arrived in Lusaka reviled as a racist and left a week later being hailed as a model of reasonableness. She and Nyerere could have been doing a duet of "getting to know you," during the past few days as they both sought to give the initiative the best possible start in life.

A key juncture will arise if the Patriotic Front hangs tough in the expected negotiations and refuses to give in the key areas of military and the election. What happens then?

There is one theory that Thatcher could go to her people, the Parliament and the world saying she tried her best, went to the heart of Africa, changed her policy and still the Patriotic Front was intractable.

So what else can she do but go ahead with whatever constitutional plan she proposes, lift sanctions, recognize and finally be done with the problem?

Machiavellian perhaps, but stranger things have happened in Zimbabwe-Rhodesia.