A key D.C. City Council committee, overriding a series of last-minute amendments proposed by Mayor Marion Barry, has approved a sweeping cable television bill that limits the role the mayor would play in awarding a city franchise that could be worth millions of dollars.

Under the 60-page measure, approved by the council's Consumer and Public Affairs Committee Tuesday night, the council would make the politically sensitive selection of a cable operator. The mayor's role would be relegated to appointing one of the 15 members of a Design Commission that will develop franchise bid requests and make recommendations to the council.

"Of course he thinks he's being frozen out," Barry press secretary Annette Samuels said of the cable bill yesterday. "The mayor was not pleased. He wants them to come up with something more equitable."

But Council member Wilhelmina Rolark (D-Ward 7), chairman of the committee, defended the legislation, saying that legislative bodies select cable operators in most jurisdictions. She said that Barry's amendments, received by the committee minutes before the panel voted, "would have completely changed the thrust of the way cable would come to the District."

Barry's amendments would have given him the right to select a cable operator and appoint the chairman of the Design Commission. Under Rolark's bill, she will appoint the commission chairman.

The passage of the cable bill breaks a two-year council stalemate over the cable issue that had triggered charges from community groups that the city was "dragging its feet" and falling far behind suburban jurisdictions in awarding a franchise. The measure would create a new multilayered bureaucracy to design a cable system for the city and includes stringent provisions to insure that cable firms will be owned and operated by members of minority groups.

The bill's affirmative action employment plan, considered the toughest ever proposed in council legislation, requires that the firm that eventually wins the lucrative franchise be required to hire minorities "proportionate with the minority population of the District." This goes far beyond most affirmative action plans which set goals, rather than fixed quotas, for minority employment. The city's population is about 70 percent black, according to the 1980 census.

Rolark, who has borne the brunt of the criticism for delays in approving cable television legislation, proclaimed yesterday that "cable was back on track" and predicted her bill would be considered by the full council by January.

But even if there is smooth sailing from now on, the city would not be in a position to award a cable franchise for at least another two years, several cable experts said. The costly and difficult task of wiring the District for cable means that most residents will not be able to receive cable television until the late 1980s, the experts said. They said the District is likely to be one of the last major cities in the country to have a cable system.

Other key provisions in the bill include:

* A public access provision that sets aside at least 10 percent of all cable channels at no charge to the city government. These channels then would be leased to community groups and private institutions or used by city agencies for community-oriented programming.

* A conflict-of-interest section that prohibits council members and Design Commission members from having a financial interest in cable companies bidding for the franchise, and prohibits private discussions between council members and cable bidders.

* A provision that officially discourages, but does not explicitly prohibit, the "rent-a-citizen" practice whereby cable firms offer stock at discount prices to politically prominent local citizens in hopes of winning the franchise.

Members of the council committee said yesterday that the antirent-a-citizen provision is intended to guard against the politically charged atmosphere that has surrounded the cable award process in such suburban jurisdictions as Prince George's County. "Rent-a-citizen is something that we definitely wanted to avoid," Rolark said. "What we're trying to do is prevent charges of influence peddling."

But an independent cable consultant said that the provision was too vague and "needs to be tightened up" if the city truly wants to prevent the practice. Howard Gan, a consultant with the Cable Television Information Center, noted that virtually the same provision had been included in regulations in Prince George's County, but it didn't prevent the county council from awarding a county franchise to a firm owned by former County Executive Winfield Kelly, even though Kelly will not be investing money that is proportionate to his 20 percent stock ownership.