Britain's new colonial administration in Rhodesia escalated pressure on the Patriotic Front today to agree to a cease-fire amid indications that several actions demanded by the guerrillas will be taken once a truce is reached.

Lord Soames, the newly appointed governor, is apparently following the same kind of carrot-and-stick diplomacy in Rhodesia as Foreign Secretary Lord Carrington has at the 14-week-old settlement conference in London, which is expected to conclude successfully this weekend.

Soames' spokesman, giving his first briefing since the governor's arrival Wednesday, said the ban on the front's two political parties would not be lifted until there is a cease-fire nor could the parties register for the elections to be held as part of an overall peace settlement. The governor has set a Dec. 31 deadline for registration.

Police briefly detained and questioned Cephas Msipa, a leading front politician, today. He organized an illegal demonstration yesterday calling an end to the ban on Patriotic Front political activities.

Bernard Pauncefort, the governor's spokesman, and Maj. Gen. John Acland, chairman of the commission to monitor an eventual cease-fire, made it clear that there would be little British control over the police or the military still prosecuting the seven-year-old guerrilla war until the agreement is signed in London.

Pauncefort refused to elaborate on just how Soames was controlling the Rhodesian civil and military officials through whom he is to administer the country. Acland said he was not in a position to give orders to Gen. Peter Walls, commander of the Rhodesian forces, nor would he comment on whether South African forces here would have to leave after a cease-fire.

Pauncefort said Soames was only informed of Mspia's detention after the event. He said the governor had "inherited" the laws of the dissolved government of Bishop Abel Muzorewa, who is opposed by the front.

Gen. Acland, asked about control of the Rhodesian military forces, said the governor has ultimate authority but the commanders "are responsible for the day-to-day conduct of their operations."

Officials hinted, however, that before sending Soames to Rhodesia to restore the breakaway colony to legality, Britain had extracted assurances from the Rhodesians that cross-border raids into Zambia and Mozambique would cease. Such raids had increased sharply, since the conference started in September.

Pauncefort said the governor had taken two specific actions: lifting bans on any British journalist barred by the former government and ordering a review of the cases of approximately 100 persons facing capital punishment.

He noted that priority matters for the governor to act upon if there is a cease-fire include legalizing the front parties, reviewing the cases of political detainees, relaxation of martial law and moving to ensure equal treatment of all parties on government controlled radio and televison.

Other priorities involve ending cross-border raids and lifting an embargo, imposed by Muzorewa, on shipments of grain to Zambia.