Britain ordered on Friday the expulsion of an Israeli diplomat it said was involved in an anti-PLO spy operation mounted here without the knowledge of the British government.

The government also ordered expulsion from Britain of a Palestine Liberation Organization official reputed to be a member of Force 17, an elite PLO unit believed responsible for terrorist acts here and elsewhere that was the target of the Israeli operation.Sources named the Israeli as Arie Regev, accredited as an attache at the embassy, and the PLO official as Zaki Howa, who has served as the organization's press officer here. Both have been ordered to leave Britain by the end of June.

The alleged Israeli and PLO activities were revealed during a criminal trial that ended here Thursday with the conviction on weapons charges of a Palestinian, Ismael Sowan, who was said to be a double-agent recruited by the Mossad, the Israeli intelligence service, to infiltrate Force 17.

Israel has not denied the anti-PLO operation. An embassy statement said only that it "regretted" the British action and that "Israel did not act against any British interests." Privately, Israel is known to be irritated that the British outcry over the operation has overshadowed the alleged terrorist activities of Force 17.

But British sources described Israel's activities as "intolerable" between friendly nations. They said that Howa was not known to be connected with any specific operation Force 17 operation but was expelled for affiliation with the organization, while Regev was believed to be the Mossad agent directly in charge of Sowan.

Sources here compared Howa's expulsion to that of Mounir Zaabi, another PLO official believed affiliated with Force 17, in April 1987. Since the PLO does not have diplomatic immunity here, either could have been arrested and detained if suspected of any crime.

The current controversy is the latest in a series of Israeli actions that have provoked outrage here.

In 1984, Mossad agents were found to be involved in an unsuccessful Nigerian attempt to abduct former Nigerian cabinet minister Umaru Dikko from London. In 1986, Mossad spirited Mordechai Vanunu, an Israeli technician who gave details of Israel's plans for a nuclear bomb to a British newspaper, out of London to Rome, where he was kidnapped and flown back to Israel. At about the same time, the Israelis were accused here of forging British passports for use by intelligence agents.

British officials also revealed Friday that another Israeli diplomat here, Jacob Barad, had been permanently barred from Britain last fall over events bearing on Friday's action. Barad was believed to be the Mossad control agent for Bashar Samara, a Palestinian also alleged to be a double-agent who had infiltrated Force 17. Barad and Samara were both quietly denied reentry to Britain while they were out of the country last fall.