Rockefeller Center Inc., the private holding company that owns Rockefeller Center in New York City, yesterday announced the signing of an exclusive contract with the British Broadcasting Corp. that will give the company rights to all BBC programmming for distribution on a new cable television network.

The company, which manages a group of Rockefeller family trusts, will distribute the BBC programs on pay cable only. This means that BBC programs will be available to both public and commercial television only after a period of exclusivity on the new network. And it raises the possibility that in cities like Washington, without cable franchises, viewers could lose access to first-run NBC offerings.

The long-term transaction, which was described here at an industry convention as worth "tens of millions" of dollars, was also said to be the largest programming deal in the history of the pay-cable industry.

BBC produces more than 5,000 hours of programming a year, more than any other producer in the world. Rockefeller Center Inc. is considered one of the largest private companies in the world.

The announcement comes on the heels of recent disclosures by the ABC and CBS corporations that they are each planning their own cultural programming networks.

Arthur Taylor and Co., an investment firm headed by Taylor, a former president of CBS, will handle the strat-up of RCTV, the programming venture formed by the Rockefeller interests.

In an interview, Taylor said the new network should not effect the Public Broadcasting Service, which has, along with public broadcasting stations across the country, provided the most significant outlet for previous BBC products distributed in the United States. These BBC shows have been highlighted with regularity on PBS and have helped attract donations to the financially troubled organization.

Taylor said the new network would be operational in January 1982 and would offer six hours of programming Mondays through Thursdays and eight hours a day on Friday, Saturdays and Sundays.

The network will offer a broad range of programs including plays, motion pictures, comedy, mystery and childrens' programming.

"This is for people who have not been satisfied by mass entertainment," Taylor said.

Bryon Parkin, managing director of BBC Enterprises Ltd., called the contract a "new direction" for BBC in the U.S. "We believe it will increase our ability to bring to the American public the full scope of programming for which the BBC has gained worldwide acclaim," Parkin said.

The new program service must still, however, find satellite space to distribute the BBC programs to cable systems across the country.