Britain today cut the price of the oil it produces from the North Sea by $4.25 a barrel, increasing the pressure on other producers of similarly highgrade crude to bring their prices down.

The reduction from $39.25 to $35 a barrel will make North Sea oil $5 a barrel cheaper than the official price for similar oil produced by Nigeria, Libya and Algeria. Those African producers have resisted attempts by Saudi Arabia to convince them to lower their prices and agree to a unified pricing structure for the Organization of Petroleum Exporting Countries (OPEC).

Britain's unprecented North Sea oil price cut was forced by the international surplus of oil produced by recession and conservation in industrial countries and by Saudi Arabia's high production levels and low prices. The Saudis price their oil at $32 a barrel, $2 below OPEC's so-called marker price, to try to push other OPEC producers into agreement on a new price structure.

Today's action by Britain, which is not an OPEC member, also links the price of North Sea oil for the first time with what Saudi Arabia charges. Previously, Britain had aligned its prices with the North African producers led by Nigeria.

This step, following price cuts earlier this month by Mexico and Ecuador of $4 a barrel for their oil, which is similar to North Sea and North African oil in quality, leaves the North African producers all alone with high official prices of $40 or more a barrel.

Industry sources said here today that Nigeria, Algeria and Libya already are selling oil at secret discounts and now are more likely to cut their official prices to keep customers. This would be a victory for Saudi Arabia's oil minister, Sheik Ahmed Zaki Yamani, in his campaign to narrow the difference between the price of heavy Persian Gulf crude and light North African and North Sea oil, these sources said.

Britain's move is expected to affect world oil markets since it exports a substantial amount of the high-grade oil from the North Sea. Offsetting its exports, however, Britain imports large amounts of lower grade oil, such as that used in power plants here.

When she visited Saudi Arabia this spring, British Prime Minister Margaret Thatcher strongly praised the Saudis for having "tried to do everything they could not to raises prices."

But Britain's price cut, decided by the government-owned British National Oil Corp. after negotiations with the multinational oil companies operating in the North Sea, could prove costly to Thatcher's government. Officials estimate that the cut could deprive the government of between $1.5 billion and $2 billion a year in revenue from taxes and royalties.

Some or all of this loss may be offset by the recent fall in the value of the pound sterling from around $2.40 to just under $2, a drop caused in part by the international money market's expectation that Britain would drastically reduce North Sea oil prices. Because oil is paid for in dollars, the revenue the British government receives will be worth more in pounds sterling.

The government had judged it would benefit from the change in currency value by cutting North Sea oil prices by just $2 a barrel, the offer the British National Oil Corp. made to the oil companies earlier this month. But, led by British Petroleum, also part-owned by the British government, the oil companies demanded a much bigger price cut.

They were losing money heavily because their income from refined oil products and resales of North Sea oil was falling far short of the cost of paying $39.25 a barrel to buy the oil from the national oil corporation. All companies operating in the North Sea are required to buy the oil through the national corporation in paper transactions at its set price even though the companies actually bring the oil up from under the North Sea themselves.

Because of the price squeeze, British Petroleum sinificantly reduced its North Sea production, according to oil industry sources, which, if that also continued would have cost the British treasury revenue. Industry sources said they expect British Petroleum's production to increase again now that the price issue has been settled.