Rhodesian police, technically under the authority of the newly installed British governor, today dispersed a peaceful demonstration by the Patriotic Front protesting the continued ban on its political activity despite the country's reversion to British control.

Neither police nor British spokesmen would say whether there had been any consultation before the action between the police and Lord Soames, the British governor who arrived yesterday to resume British authority in the former breakaway colony.

As is usual in Salisbury, estimates on the size of the demonstration varied according to the political view of the estimators, with police saying 500 to 600 and a Patriotic Front spokesman saying about 4,500. Journalists agreed that there were between 1,000 and 2,000.

The police action poses a touchy political problem for Soames, who is governing under virtual dictatorial powers even though the Patriotic Front has not yet accepted a British cease-fire plan, the only remaining obstacle to an overall peace settlement with the former Salisbury government of Abel Muzorewa.

Soames is now in the position of carrying out laws enacted by Muzorewa under which thousands of persons have been detained, and political activity has been proscribed.

A British spokesman said the political ban would be maintained until the Patriotic Front accepted the cease-fire.

The spokesman declined to say what would happen if the Rhodesian military now under Soames' command attempted to continue its practice of raids into Zambia and Mozambique to disrupt Front activities in those countries.

Britain has established set of priorities for Soames' initial actions which reportedly include ordering an end to cross-border raids, release of political prisoners and lifting the Muzorewa government's embargo on grain shipments to drought-stricken Zambia.

Soames' first full day in office, however, was a low-key affair as he appeared to be feeling his way and perhaps waiting for the successful completion of the London talks. He had indicated as much to reporters yesterday, saying, "I don't want to rush in where angels fear to tread," especially because of the continuing war.

He spent most of the day talking to officials of the Muzorewa government, which stepped aside Tuesday to make way for Soames. An hour-long meeting with Muzorewa covered the process of taking over the administration follwed by a session with Cabinet chief George Smith on the functioning of the civil service, which is to carry out the governors' policy during a three-month transistion.

Cephas Msipa, who called the Patriotic Front demonstration this mourning, said his organization had been disappointed that Soames had not lifted the political ban when he spoke to the nation last night.

He said the police, who blocked off the downtown road where the demonstrators gathered, had threatened to assault the protesters unless they broke up.