The Prince George's County Council voted unanimously yesterday to approve the first of the county's two $30 million cable television franchise agreements, clearing the final hurdle for cable service to much of the southern end of the county.

Representatives of MetroVision Inc., an Atlanta-based firm that won the right to build the southern area system after a sometimes bitter controversy last fall, promised the council that some residents would begin to receive cable service as early as this November. Company officials said that the entire franchise area, which is bordered roughly by Central Avenue, Rte. 301 and the District line, would receive service within three years. Beyond those areas, residents may have to pay an additional fee for service, depending upon the density of the population near their homes.

First to receive service, according to MetroVision attorney Russell Shipley, will be residents of inner Beltway areas between Pennsylvania and Central Avenues, in communities such as District Heights and Capitol Heights.

Officials said that negotiation of the north county franchise award, to Storer Cable Communications Inc., of Miami, was delayed because of a citizens group's efforts to have the award overturned by a voters' referendum. That effort failed in February, however, and county officials said that the agreement should be reviewed by County Executive Lawrence Hogan within the week.

According to Dolores Early, the departing director of the county's cable television commission, the agreement gives the county 5 percent of the company's gross revenues each year. In the first year of service, vice president Craig Magher said, the company should gross about $3.6 million, which would result in payment to the county of about $180,000.

Under the agreement, south county residents will be able to receive about 70 channels immediately and 112 in the future. Basic monthly charges range from about $2.95 to $10.95, with most extra services such as Home Box Office available for $7.95 each.