Britain will invite the warring factions in Zimbabwe-Rhodesia next week to meet here in September and consider a new constitution under which Britain could grant its former colony legal independence with a black majority government.

Prime Minister Abel Muzorewa's recently installed multiracial government in Salisbury and the Patriotic Front guerrilla forces led by Robert Mugabe and Joshua Nkomo will be asked to send delegations to the constitutional conference, which will be chaired by Britain's foreign minister, Lord Carrington.

Prime Minister Margaret Thatcher's Cabinet approved these steps today after Thatcher and Carrington briefed the Cabinet on the peace initiative worked out by Britain and black Africa at the Commonwealth conference in Lusaka, Zambia, earlier this week. The Lusaka plan calls for Britain to draft a new proposed constitution, present it to all the parties in the conflict for their agreement, hold new elections, restore the country to lgeality and grant its independence.

The British envoy, who has been Thatcher's contact with Muzorewa's government, will return to Salisbury this weekend to seek Muzorewa's agreement to send a delegation to the conference. Nkomo and Mugabe will be pressured to attend by the leaders of the neighboring African nations that have supported their struggle against the Salisbury government.

Since each leader will be free to choose the members of his own delegation, Muzorewa's could include, as a representative of Zimbabwe-Rhodesia's white minority, Ian Smith, the former prime iminister who unilaterally declared independence and broke with Britain in 1965. Smith also engineered the multiracial "internal settlement" that put Muzorewa in power earlier this year with a constitution reserving considerable power for the white minority, a formula unacceptable to the Patriotic Front rebels and the rest of Black Africa.

Britain's Foreign Office is drafting a new constitution that would resemble more closely those of other former colonies that have gained legal independence from Britain. While it is still expected to protect a disproportionately large number of parliamentary seats for white Rhodesians - perhpas 20 of 100 seats for about 4 percent of the population - it would no longer give the whites the power to block constitutional changes or guarantee them control of the civil service, Army, police and courts.

The constitutional conference here is expected to last only a few weeks, although it will operate under no time limit. It also is expected to be fractious, with Muzorewa on one side and Mugabe and Nkomo on the other struggling for the upper hand in the formation of a new constitution and government.

Although she knows there are very difficult problems to overcome, Thatcher is known to want this process to be well under way, if not nearly completed, before her Conservative Party holds its annual conference early in October and Parliament returns to session after its summer recess later that month.

A vocal minority of Conservative members of Parliament, who are concerned about the future of Zimbabwe-Rhodesia's whites, are angry that Thatcher did not simply confer legality on Muzorewa's government asshe seemed inclined to do before becoming prime minister.

If restoration of legality for Zimbabwe-Rhodesia were not imminent, and in a form giving some protection to the white minority, these critics are likely to try to embarrass Thatcher at the party conference and in Parliament. They also will insist that British economic sanctions against Zimbabwe-Rhodesia will be abandoned when they come up for renewal in Parliament in November, which Thatcher has already said is a political likelihood.

Although Thatcher was persuaded by Lord Carrington to abandon unconditional support for the Mzuorewa government and seek an all-party solution well before the Commonwealth conference in Lusaka, details of her change in policy were kept secret to avoid a right-wing outcry here before she left for Africa.

Thatcher has insisted that she has not really deviated from her determination to find some way to restore Zimbabwe-Rhodesia to legality and lift the economic sanctions. She says she now is going about it in a different way.

There has been widespread speculation here, as there was in Lusaka and Salisbury this week, that Thatcher actually has maneuvered the Patriotic Front leaders, whom she has denounced as Soviet puppets in the past, into a difficult position.

Either they must agree to a new constitution and independence process that may well not give them the role in Zimbabwe-Rhodesia's government or control of its army that they seek, or they face the prospect that Britain will go ahead with the new constitution anyway on the grounds that the Patriotic Front would not cooperate in a peace plan initiated by the African leaders supporting them.

That scenario, however, would leave a new government still at war with the rebels, whether or not they could count on the same support from neighboring black African states.