The Chesapeake & Potomac Telephone Companies had sought approval for steep increases in phone rates from regulatory agencies in the District of Columbia, Maryland, Virginia and West Virginia even before the historic agreement was announced to break up American Telephone & Telegraph Co.

These requests, still under review by all four regulatory authorities, are described as reflecting inflation, shifts in federal regulatory policies, increased competition in the communications industry, and other factors. The proposed rate increases in the District, Maryland and West Virginia have not been granted. Virginia allowed a rate rise to go into effect, but reserved the right to order refunds if it finds the higher charges unwarranted.

Whether the AT&T antitrust agreement will alter the outcome of these proceedings is unclear, though the possibility has been raised in the District and Maryland.

In the District, C&P has proposed a $75.1 million revenue increase, its biggest ever. The price of its most widely used local residential service--allowing unlimited calls throughout the metropolitan area--would rise by 80 percent, from $8.18 a month to $14.76. Pay phone calls would cost 25 cents instead of 15 cents. Calling information would jump from 10 cents to 25 cents. Minimum phone installation charges would go from $15.40 to $43.05. C&P describes its proposal as a 34 percent overall increase.

D.C. phone rates previously were increased by 7.1 percent last June 26, according to a C&P spokesman.

In Maryland, C&P is seeking an overall 26 percent rise to boost revenue by $211 million. The Aug. 27 request would increase basic residential service rates from $9.85 a month to $13.80. Pay phone calls would rise to 25 cents from 15 cents. Residential installation would climb from $42.35 to $64.90. According to C&P, rates in Maryland last rose by 4.1 percent about a year ago.

In Virginia, the State Corporation Commission authorized a 10.7 percent surcharge on phone rates Nov. 10 to increase C&P's revenue by $77.6 million. State officials are still considering whether to modify that decision and order refunds. According to C&P, basic residential service charges rose from $10.65 a month to $11.79. The last major increase in Virginia rates was a 5 percent rise on Dec. 19, 1980, according to C&P.

In West Virginia, C&P is seeking a 25 percent overall increase to gain $69 million in additional revenue. C&P says its rates last rose in West Virginia in 1980, by 11 percent.