Defying the tradition that one chamber does not interfere in the other's affairs, the House voted over-whelmingly yesterday to kill money for the Senate's new office building.

The 245-to-133 vote to delete $54.8 million for the building from a $6.8 billion supplemental appropriations bill startled many Capitol Hill veterans. The noninterference tradition - known as comity - is so strong that Appropriations Committee Chairman George N. Mahon (D-Tex.) said that, in 44 years in Congress, this was the first time he had seen it violated.

The House action irritated several senators. "It's a dirty trick," said Senate Majority Whip Alan Cranston (D-Calif.). and he speculated early in the day that the Senate, which is to work for the next two weeks while the House adjourns for a summer recess, might not agree to the adjournment resolution necessary to let the House go home.

The Senate didn't, however, and the House adjourned until Sept. 6, while the Senate will adjourn for about a week around Labor Day.

But Sen. William Proxmire (D-Wis.), a vigorous foe of the $135 million building who gave it his "Golden Fleece of the Month" award, said comity was "a ridiculous precedent" and "the House of Representatives has every right to step in when it sees that the interest of the taxpayers is being flouted by the Senate."

Several reasons were given for the unprecedented step by the House. House Majority Whip John Brademas (D-Ind.) cited a rash of editorials decrying the building of a new Capitol Hill edifice while the country is trying to cut spending and fight inflation.

The building, to be named after the late Sen. Philip A. Hart (D-Mich.). is scheduled to have elegant paneling, office suites with 16-foot-high cellings, a third Senate gym, indoor tennis court and a rooftop restaurant for senators only.

Brademas said press reaction "created enough unhappiness back home" to cause House members to vote the money down. Brademas said a second reason was that, "Clearly, House members won't occupy the Senate office building."

The whole supplemental appropriations conference report almost went down to defeat because of the building. The bill contains programs usually voted for overwhelmingly, such as money for salaries for military and civilian personnel, Small Business Administration disaster loans, veterans compensations and pensions, government retirement pay and economic development assistance money.

The vote on the conference report was 193 to 189 against the bill when the gavel went down. House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) rushed to the floor to turn the vote around.

Republicans, in a bit of last-day-before-the-recess silliness that sometimes comes over the House, began singing to the tune of "The Farmer in the Dell," "The speaker's in the well, the speakers in the well, he's got to save the building, the speaker's in the well." O'Neill did save the bill, and the final vote was 198 to 191 for it.

The vote against the building cut across party lines. Rep. Morris K. Udall (D-Ariz.) explained, I was one of those who 10 years ago was urging more staff. Now I'm convinced we've gone far enough. It's one of the natural laws that personnel expands to fill space. Maybe if they slow down, we'll slow down over here."

The Hart building is already under construction, and the $54 million was to furnish and finish it.

Rep. barbara Mikulski (D-Md.) explained her vote against the building by saying. "I couldn't in good conscience vote for three gyms for 96 men until we get the Equal Rights Amendment." There are two women senators.

And Rep. John D. Dingell (D-Mich.) simply admitted he was mad at the Senate. "They caused me a lot of trouble on the natural gas bill. If they think I'm going to vote them more space they're making a mistake."

Rep. Tom Bevill (D-Ala.) simply said, "This should just be called Proposition 13 Day."

In other action the House also refused, by voice vote, to allow civil service pensions for employes of the House and Senate congressional campaign committees, another move that has been widely criticized.

The supplemental appropriations bill differences about the building must now be resolved between the House and Senate. Nobody was too sure how that would come out, but the Senate did seem more divided on the issue.