The Democratic-controlled House defied President Reagan yesterday and in the name of fairness and reducing the deficit voted to limit July's scheduled 10 percent tax cut to a maximum of $720 per return.

But the bill, which would raise $6 billion in the 1984 fiscal year, mainly from households with incomes over $50,000, is unlikely to become law. Even if it passes the Republican-controlled Senate, an uncertain prospect, its sponsors lack the votes to overcome a promised presidential veto.

The House vote was 229 to 191, well under the two-thirds needed to override the president. Twenty-nine Democrats voted against the bill in what Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) had made a referendum on Reagan's economic policies. No Washington-area Democrats were among the defectors. The Republicans were unanimous in opposition.

The scheduled July 1 tax cut is the third and last installment of the 25 percent rate reduction Reagan pushed through Congress in 1981. Tax and domestic spending cuts were central to his campaign in 1980 and remain his favorite themes. He has repeatedly said he will brook no change in the tax cut, which he says has been crucial in fueling the economic recovery.

Because most members agree the tax-cut cap pushed by O'Neill will never become law, the House debate yesterday was largely a symbolic and political exercise.

Democrats said that the 10 percent third-year reduction, which would save some upper-bracket taxpayers as much as $3,736, was a Republican giveaway to the rich with borrowed money. But the bill to cap the cut at $720 would also affect millions of households with incomes under $50,000; they make up roughly half those that would be involved though they would contribute only about an eighth of the expected revenue.

The Republicans cited such figures as these to prove the Democrats were pinching the middle class, "the people who pull the wagons," as Rep. Phil Gramm (R-Tex.) called them.

Minority Whip Trent Lott (R-Miss.) said it was an "Orwellian" distortion of language for the Democrats to call their bill the "Tax Rate Equity Act of 1983" because "it's just a tax increase."

But Majority Leader James C. Wright Jr. (D-Tex.) said the bill would not mean a tax increase, only a reduced tax cut for some when withholding rates are adjusted next month. He said Reagan, whom he called "the Babe Ruth of deficit spending," wants to "veto a bill that would reduce the federal deficit by requiring the privileged, the affluent, to accept a tax reduction of only $700."

Wright said Reagan, through spending and tax cuts combined, has perpetrated "the most retrogressive redistribution of wealth in America's history, from the pockets of the poor into the pockets of the rich," and that capping the tax cut would begin reversing that while also restraining growth of the deficit.

The fiscal 1984 budget resolution approved by the House and Senate yesterday calls for $12 billion in new revenue in fiscal 1984, and the Democrats said the tax-cut cap is the only large-scale bill around for moving toward that.

If enacted, the limitation of the tax cut would affect about 8 million of the 95.5 million tax returns filed each year. For married couples with two children who itemize deductions, the cap would go into effect above an adjusted gross income of $46,494.

For single taxpayers, the impact would be felt beginning at an adjusted gross income of $35,714. Taxpayers with lower incomes would not be affected because their scheduled cuts would be less than $720.

The House vote demonstrated the ability of O'Neill and Wright to keep their troops in line even when many of the Democratic rank and file were less than enthusiastic.

Before the vote, O'Neill, Wright, Majority Whip Thomas S. Foley (D-Wash.) and Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) circulated a "Dear Colleague" letter saying the administration's refusal to endorse any major new revenue measure for fiscal 1984 was a prescription for "$200 billion deficits as far as the eye can see." This show of unity by the leadership followed weeks of backstage discussions, in which Rostenkowski was known to be reluctant to bring out such a bill.

In a gesture to nervous Democrats who feared they would be labeled tax-raisers and big spenders, the leadedrship accepted an amendment tying the tax-cut cap to a reduction in spending of an equal amount, but this had no real significance because, according to Wright, the spending cuts called for are those already included in the newly approved budget resolution, not additional cuts. Rep. Barber B. Conable Jr. (R-N.Y), leading the fight against the bill, called this amendment a "flim flam."

A recent Washington Post-ABC news poll had 47 percent of respondents favoring a tax-cut cap, and 40 percent opposing one.