Britain yesterday indicated that it may be about to cut the price of North Sea oil, possibly triggering the reduction in world oil prices that has seemed inevitable since last month's meeting of the Organization of Petroleum Exporting Countries (OPEC) ended in chaos.

State-owned British National Oil Corp., which markets British North Sea crude, informed its customers by telex that it would be in a position to make a new price recommendation Friday. Industry sources said they expected a cut of $3 to $3.50 per barrel from the present $33.50.

"Once the British start it, the Saudis, the Nigerians and everybody else will reduce their prices," John Lichtblau, president of the Petroleum Industry Research Foundation, predicted yesterday. "The Saudis clearly have wanted to reduce the price, and have seemed impatient for the British to go first."

The big question, government and industry analysts agreed, is whether world oil prices, which have been based on an OPEC benchmark price of $34 a barrel for Saudi light crude, will stabilize again in the $29-to-$30 range or whether further cuts will follow.

"Will the first cuts lead to a price war, or will they help OPEC restore stability to the market?" asked a government official who tracks international oil markets.

Underlying that question is a test of nerves that has pitted the oil-producing countries against the major oil companies since the first of the year.

During January, OPEC production dropped to about 17.1 million barrels a day, U.S government sources say. Since the breakup of the OPEC meeting three weeks ago it has fallen to the 16 million to 16.5 million range, they add. Some industry sources say they think it now may be as low as 15.5 million.

"That's an explosive situation for some of those countries," a U.S. government source said. "Some of them need to sell twice as much as they are exporting at the moment just to squeeze by."

By comparison, OPEC's unsuccessful effort last month was aimed at setting an overall cartel ceiling of 17.5 million barrels a day, with individual production quotas for each nation. OPEC production hit a record 31 million barrels a day in 1979.

Part of weak demand for OPEC oil is attributed to the unusually warm winter here and in Europe.

But a more important factor, according to government sources, is that the major American and European oil companies have been drawing down their inventories by about 2 million to 3 million barrels a day more than the seasonal average.

"The companies are sitting back and just waiting for prices to drop," a government official said. "This has become a waiting game of who is going to give in first. Does a country's need for revenue force it to give price cuts before a company's inventories get as low as it dares reduce them?"

"It's a question of who blinks first," Lichtblau said. "There's only a fairly short time that some of the OPEC countries can live with this low level. On the other hand, the general belief in the industry is that this inventory reduction could go on a few more months, not just one more month."

Another factor that could favor lower oil prices is a growing belief within the oil industry that, even with an economic recovery in the United States and Europe, worldwide oil demand is likely to be no higher this year than it was in 1982.

Officials of a major international oil company are projecting total worldwide demand for oil in 1983 at 45.7 million barrels per day, a drop of 200,000 from last year. While they suggest that this will result in a "modest increase" in demand for OPEC crude to an average of about 19.3 million barrels a day for all of 1983, compared with 18.8 million in 1982, it would not produce a major strengthening of the world oil market.

In a related development yesterday that added to the psychological pressure on OPEC, Ashland Oil Co. and Marathon Petroleum Co. followed the lead of Texaco Inc. in reducing by an additional $1 per barrel the price they pay for the highest quality domestic crude oil. Texaco on Monday cut the price it pays for west Texas-New Mexico sour crude, similar to Saudi light, to $29 a barrel.