Construction has started on a $26 million headquarters for the law firm of Arnold & Porter - a modern structure that will include virtually everything a counsel might want: interior atrium, private offices and balconies on all levels, retail space on the ground floor and squash courts.

The Oliver T. Carr Co. is developing and leasing the building at 1200 New Hampshire Ave. NW, which will be named for one of the law firm's founders, Thurman Arnold. Under President Franklin Roosevelt, Arnold was a federal judge and assistant attorney general.

Arnold. Paul Porter and former Supreme Court Justice Abe Fortas started the law firm in 1947. It has become one of the five largest law business in Washington, with 125 lawyers and more than 200 other employes currently located in several buildings.

Murray, Bring, chairman of the law firm's leasing committee, said yesterday that Arnold & Porter expects to begin consolidating all offices in the new headquarters in the fall of 1976. About 150,000 square feet - 62 percent available office space - will be occupied by Arnold & Porter.

And, in recognition of how rapidly the law business is expanding, Arnold & Porter will have enough room to house 174 lawyers in appropriate quarters.

The firm doubled in size from 45 to 91 lawyers between 1965 and 1973 and has added more than 30 lawyers since.

According to Carr Co.'s director of operations, Philip Carr, his firm is developing the Thurman Arnold building for a partnership of owners called Square 70 Associates that consists of restaurateur Ulysses (Blackie) Auger, George Hyman Construction Co. President James Clark and Carr Co. President Oliver Carr Jr. An Auger-owned Marriott hotel is to be built adjacent to the law firm tower, and the buildings will be linked by a second floor skywalk.

Hyman is contractor for the building, designed by the architectural firm of Weihe, Black, Jeffries and Strassman. The eight-story building will feature a brick facade and 17,000 square feet of retail space.

Enviornmental Planning & Research Inc. has been hired by Arnold & Porter to develop interior designs.