Bills for Virginia customers of the Chesapeake & Potomac Telephone Co. will jump 9 percent starting Friday because of an interim $66 million rate increase granted today by the Virginia State Corporation Commission.

The $11.79 monthly fee that C & P residential and business customers in Northern Virginia now pay for unlimited calls in the Washington area will rise to about $12.85. Long-distance rates for calls within Virginia also will go up 9 percent.

Today's action -- called a "pretty big-size increase" by a commission spokesman -- comes on top of a 10.7 percent surcharge that was approved by the commission and added to Virginia telephone bills a year ago.

But the new increase represents less than half the $133.5 million that C & P requested of the commission last August.

The commission also failed to act on the company's request to increase the cost of other services, such as installation and maintenance.

Additionally, it delayed, pending further hearings, a request to base charges for WATS (Wide Area Telephone Service) on frequency of use rather than a flat fee. The service allows customers to make a large number of long-distance calls at rates below regular long-distance service.

"We're kind of disappointed -- we got less than half of what we asked for," said Ray Gross, a C & P spokesman here "We asked for this because we need to increase our return on equity in order to compete for investors' dollars. This will not put us in a competitive position."

Unless the full increase is awarded, C & P will have to reexamine its budget of new construction, which totals $350 million this year, Gross said.

The interim action means the commission will hold a public hearing on the full C & P request Jan. 5 and that the monies generated by this week's increases can be refunded if the company fails to demonstate that its revenue requirements justify them. But the commission strongly hinted in a statement that no refunds would be forthcoming.

According to the statement, the commission found the full C & P request "too high," but based on data the company has already supplied, "there is a reasonable probability that upon full investigation and hearing an increase in annual revenues of $66.5 million will be found justified."

Gross said: "We're going to go in there again [in January] and try to reaffirm our original case."

The District of Columbia Public Service Commission approved an 18.6 percent phone rate increase last April, and C & P President Robert Allen has said the company may ask for another increase in the city next March. A C & P request for a 27 percent increase is pending before the Maryland Public Service Commission.

The increases are in part a byproduct of the upcoming divestiture of AT&T scheduled for January 1984 when the national corporation will spin off its 22 locally owned companies. C & P spokesmen have said they need additional revenue so the company can be in healthy financial shape when divestiture takes place.

Although the public hearing on the Virginia request will not take place until January, protests have already been filed with the commission by the state attorney general's office, several large industries, and the Department of Defense. The Pentagon has one of the largest telephone bills in the state.