A growing scandal over illegal shipments by British oil companies to Rhodesia is engulfing some of the most prominent figures in public and private life here. It even threatens to compromise the remaining British influence in black Africa.

Each day brings fresh revelations in what the conservative Times of London yesterday called "a shabby story" that threatens "the integrity of government."

The latest target is former Prime Minister Harold Wilson, who has maintained within the past week that he was "hoodwinked" by the government-owned British Petroleum as well as Royal Dutch Shell, which is 40 percent British-owned.

These concerns have supplied Prime Minister Ian Smith's government with about half its oil imports despite a ban ordered by Wilson after Smith unilaterally declared Rhodesian independent from Britain in 1965, according to undisputed evidence made public in the controversy.

Wednesday night, a former Wilson minister declared flatly that Wilson and others in his cabinet were told "in writing" how the sanctions were breached.

"It was not Sir Harold who was hoodwinked," the Times thundered yesterday, "but the British public and anyone else who gave credence to British statements."

The public record is filled with evidence that this is a bipartisan scandal, that Conservatives like Labor chose to look the other way while BP and Shell broke the ban on trade with Rhodesia for 12 years. But the Tories, in power from 1970 to 1974, made clear, unlike Labor, that they disliked the trade sanctions and sympathized with Smith.

The evidence now being aired shows that BP and Shell ignored the embargo until July 1977, either by direct shipments or briefly through a French intermediary.

They supplied about 50 percent of Rhodesia's oil imports, according to evidence coming out in newspaper reports. The rest came, according to the reports, from Mobil; Caltex, a joint subsidiary of Standard Oil of California and Texaco; and a unit of the French Compagnie Francaise des Petroles.

The United States, while imposing no specific ban of its own, has accepted a United Nations ban on commerce, including oil, with Rhodesia.

BP and Shell finally ordered their South African shippers to stop supplying Rhodesia with oil last summer when the British government set up an inquiry into the business.

The inquiry, run by a lawyer, Thomas Bingham, is now complete. But how much its 600, still-secret pages will disclose is a question. Bingham never called on Wilson to testify. Nor, according to news reports, did Bingham call on Denis Greenhill, a key government and oil company official.

As the top civil servant at the Foreign Office from 1969 to 1973, Greenhill has said "there was very close contact with BP" and that he thought "the Foreign Office knew of the swap arrangements."

The "swap arrangements" were the short-lived BP-Shell device to slip oil to Rhodesia through a French middleman.

Since leaving the Foreign Office, Greenhill, now a lord, has sat on the BP board as one of two government directors. There he gets $11,700 for services.

Still another former official who has straddled the oil arrangements is Alan Gregory. BP has said that Gregory, when a ranking civil servant in the Power Ministry, was told in detail of what BP has called its "cosmetic" shipments through the middleman. Two years later, Gregory also moved over to the oil giant and is now deputy chairman of the executive committee of BP Trading. The company, 51 per cent owned by the government, will not reveal his wage.

According to the reports which have come out in the past week, government ministers learned of the BP-Shell breach early in 1968. The companies' bosses are said to have told George Thomson, then the Commonwealth Secretary, that the embargo had been broken and that they would switch to what they call the "transparent" device of a middlemen.

Thomson, who has also been rewarded with a peerage, now asserts:

"I conveyed in writing to the prime minister (Wilson) and other ministers most directly concerned a full account of all that passed at my meetings on behalf of the government with the oil companies."

As recently as a week ago, Wilson, now a back bench and elder statesman, told the British Broadcasting Corp. that Rhodesia got its life-giving oil because of the French and the lack of pressure on Paris.

The Bingham report has been given to the Director of Public Prosecutions to determine if anyone committed a crime. Breaching the ban on Rhodesian trade could bring jail sentences up to two years.

The standard defense, offered by Thomson and Frank McFadzean, former Shell chief, runs like this: Britain could not stop the trade without blockading South Africa and what was until 1975 Portugese Mozambique. Oil coming to those countries was bound to be shipped to Rhodesia.

"A collision course with South Africa," Thomson has said, would threaten "large British markets and investments."

With white minority rule in Rhodesia apparently nearing its end, the scandal here has a somewhat academic flavor. But there could be long range consequences for Britian in Africa since London appears to have condoned what Black Africa regards as a racist government.

As recently as 1976, Britain told the United Nations that BP and Shell had assured London no British oil was flowing to Rhodesia. Michael Palliser, now the top civil servant at the Foreign Office, even thanked McFadzean personally for these assurances.

In fact, at that time, BP and Shell had dropped the middleman device and had resumed their direct shipments to Smith.

The Guardian observed in an editorial yesterday:

"The deceit was magnified by appeals to other countries to behave with British rectititude. Until this shameful episode is purged by a public inquiry, the other countries concerned (and indeed the United Nations, pressed by Britain into making sanctions mandatory) can only have scant regard for the value of Britain's word."