Britain's oldest Sunday newspaper, the Observer, has again been threatened with closure four years after it was rescued from financial failure by American oil millionaire Robert Anderson.

The management of the 189-year-old newspaper, which is owned by Anderson's Atlantic Richfield oil company, today gave its employes formal notice that it would shut the paper down in 90 days because one labor union representing about 60 of the 500 employes has blocked plans to streamline the newspaper's production.

Atlantic Richfield already has invested an estimated $20 million in improving the newspaper's editorial quality, circulation and advertising. However, company officials decided they could not afford the extra cost of printing the paper in sections throughout the week rather than altogether on Saturday night. One union, the National Graphical Association, refused to agree to the Observer's proposal regarding compensation, hours and staffing for making this change.

It remains uncertain whether the 90-day notice of closure is only the Observer's final drastic negotiating tactic, whether Atlantic Richfield really intends to shut the Observer down, or whether it would sell to any of several wealthy press lords believed eager to acquire the newspaper, which has a circulation of more than 1 million. e

The prospective buyers reportedly include Australian Rupert Murdoch, publisher of Britain's most outrageous and largest-selling tabloid, the Sun. He also publishes the New York Post and Village Voice in the United States. a

The Observer dispute is symptomatic of chronic production and financial problems facing many of Britains national daily and Sunday newspapers published on and around Fleet Street in central London.

Despite big circulation gains enjoyed by many of the papers in recent years, half are believed to be losing money because of inefficient management, outmoded technology and union protection of overmanning and restrictive work rules.

A number of Fleet Street papers are kept afloat despite their losses by owners willing to pay the price for the prestige of being press barons. Both the Observer and the Times newspaper (owned by the Toronto-based Thomson organization) have been subsidized by the oil revenues of their parent organizations.

Equipment breakdowns and wildcat labor disruptions have cost Fleet Street newspaper 75 million lost copies so far this year, 90 million last year and 155 million in 1978. This does not include the complete shutdown of the Times and Sunday Times for 11 months during a labor dispute over the introduction of new technology. Despite large pay raises given to employes in the settlement of the Times dispute, its management recently complained that union leaders have failed to keep their promise to negotiate a way to operate millions of dollars worth of computer equipment bought by the Times but never used.

During the Times strike, the circulation of the steadily improving Observer increased from 800,000 to about 1.3 million, and it has kept much of that gain since the Sunday Times reappeared last year. But printing the extra papers only increased the Observer's losses, despite gains in advertising, because of the expensive way it is printed.

In its statement, the Observer management told employes that the newspaper would stop publishing and that their jobs would be lost in 90 days. It said it could not afford to meet the union's demands "now or in the future" despite the heavy investment it has already made in the paper.

Rejecting the Observer's final offer last night, the union's general secretary, Joe Wade, said, "If we back down every time a Fleet Street management threatens us with closure if we will not accept their terms we might as well not bother negotiating." He said his union did not back down at the Times or other newspapers under those circumstances, "and we are not backing down at the Observer."