At least three private companies are seeking a franchise from the City of Alexandria for a cable television system even before the city has finished drafting a proposed law to regulate the service.

One of the companies, Community Cable Vision Inc., is headed by James M. Thomson, former majority leader of the Virginia House of Delegates who was defeated in a reelection bid in November. A second company, Alexandria Cablevision, is represented by a former chairman of the Federal Communications Commission. The third company, Arlington Tele-Communications Corp. (ARTEC), is scheduled to start cable service in Arlington in July.

Alexandria attempted to pass a cable television ordinance in 1974, but the effort was dropped because of lack of public interest. Now, with the Arlington system about to start after years of delays, Alexandria officials say the City Council could pass an ordinance by the end of this year. Cable service could start in some parts of the city by late 1981 or early 1982.

Cable television, which transmits pictures by means of a coaxial cable instead of a normal antenna, was originally popular in rural areas that received poor reception. In recent years, however, it has started to appear in urban areas because it can offer clear pictures and special services such as sports events and first-run movies without commercial interruption.

Because cable television makes use of public rights of way such as streets for its cable, localities pass laws to regulate the system and derive some public benefit in return for granting a private company a franchise.

"You've got to strike a balance between protecting the consumers and private property and what is economically feasible" for the operators, remarked Howard Middleton, the city attorney principally in charge of drafting a new ordinance for Alexandria.

The ordinance will deal with matters such as duration of the franchise and conditions for renewal, the number of television channels which will be provided, including those that will provide "public interest" programming, and such political hot potatoes as whether the city will get involved in rate regulation.

"That issue of rates is up for grabs," said Middleton.

Alexandria City Council members Robert L. Calhoun and Donald C. Casey, the leading proponents of cable television on the panel, believe competition is sufficient so that rate regulation by the city is not needed now. This position has also been adopted by the Alexandria Consumer Affairs Commission.

Arlington does regulate rates charges customers of cable television much as rates for public utilities are regulated.Industry officials, however, believe that rate regulation injects politics by tending to encourage applications only from companies with the local political clout to get rate increases approved.

Spokesmen for the companies seeking a franchise refused to disclose details of programming they might offer Alexandria residents for fear it would give their competition an edge, but all said the Alexandria had great potential as a cable television market.

Frederick W. Ford, chairman of the FCC in 1960 and 1961 who has been trying to get a cable television franchise in Alexandria since 1970, said his system would provide a service similar to that which will be offered in Arlington by ARTEC, including programs from stations as far away as Atlanta and San Francisco.

"You can cater to the needs of many diverse groups and each of those subscribe for their own purposes," said Ford.

Thomson, president of Community Cable Vision Inc., said his company is still getting organized and added that the programming which would be offered "will be geared to what the city wants to produce." He would not elaborate.

John D. Evans, chief operating officer of ARTEC, said he would take "a hard look" at entering the Alexandria market but said he would not do so under terms of the 1974 ordinance, because it was so restrictive that he could not make a profit.

Differences between the cable companies and Alexandria are already becoming apparent in drafting of the new ordinance. Ford, for instance, would like to see a much longer period before he must begin operations after the franchise is granted than Alexandria appears willing to permit. After the franchise is awarded, the company must receive a certificate of compliance from the FCC, and cable operators usually prefer to wait until they have the certificate before starting construction. Alexandria, however, wants construction to start before the certificate is issued.