Taxicab fares in the District of Columbia will increase 10 cents on Sunday for all trips of any length, the D.C. Public Service Commission ordered yesterday.

The increase, the first in 14, months, means the cost of a one-zone trip will go from $1.45 to $1.55 and a trip from downtown to the outer edges of the city from $3.55 to $3.65. There will be no increase in the cost of traveling through additional zones beyond the first zone.

By coincidence, the increase will go into effect just two weeks before an identical 10-cent boost in the minimum cost of riding the Metro subway and bus system, the principal competitor of the city's taxicab industry. Basic nonrush-hour Metro fares will go from 50 to 60 cents starting Jan. 4.

In its 2-to-0 ruling yesterday, the PSC said cab fare increase is an interim measure to help cab drivers absorb inflationary costs, until an eventual decision is reached on an industry group's application for a 20 percent across-the-board increase.

The larger increase could come early in 1981, according to Brian Lederer, people's counsel, whose office represents the public arrange the stopgap increase. He praised the PSC for "a responsible decision."

"We are pleased to have something," thing," said William Wright, president of the Taxicab Industry Group, which also pushed for the increase. "I am sure this will be a little help. But we hope to follow through on getting more."

Alfred D. Farmer, a former antique restorer who has been driving cabs part time since 1968 to supplement his retirement income, applauded the decision when told of it by a reporter. "Anything we get is helpful," he said, "but it takes so long to do anything. They have to ponder it and ponder it and do so much research on it."

There were no official figures indicating what the new increase will yield to the city's 7,593 taxicabs and 9,799 licensed drivers. A driver who carries 25 passengers in a workday will collect a total of $2.50 additional in fares.

Unlike most cities, where drivers work on wages and commissions paid by cab-fleet operators, Washington cabs are owned or leased by their drivers, who collect the fares, pay the expenses and keep what is left over as profit. Among those costs has been the rapidly increasing price of gasoline -- up about 25 cents a gallon since the last cab fare increase in October 1979.

Also unlike other cities, taxicab-fare meters are prohibited here by Congress, and fares are collected under a complex geographic zone system.

PSC Chairman Ruth Hankins-Nesbitt was joined in voting the fare increase yesterday by PSC member Wesley H. Long.The third PSC member, Patricia Worthy Clement, was absent.

Once beofe, in June 1979, the PSC granted an identical 10-cent-a-ride fare increase without holding a hearing. It did so after militant cab drivers, angry about the growing gap between increases, organized rallies and a motorcade through downtown and threatened to organize a strike. Four months later, the PSC approved a fare increase from $1.30 to the present $1.45 for a one-zone trip.