A strong majority of the House has lined up in support of legislation to index the income tax system to inflation, as approved by the Senate Thursday, but the chairman of the Ways and Means Committee said yesterday he will fight efforts to bring the issue to the floor.

Rep. Willis D. Gradison Jr. (R-Ohio) has 223 co-sponsors for his major structural change designed to prevent the steady lifting of taxpayers into higher brackets as their incomes rise with inflation. The Senate voted 57 to 40 Thursday night in favor of an amendment to the tax bill that would impose indexing in 1985.

Ways and Means Chairman Dan Rostenkowski (D-Ill.), meeting with reporters yesterday, acknowledged that the Gradison proposal would sweep through the House, but aides stressed later that he would use his control of a majority of votes on the panel to prevent the issue from reaching the House floor.

In the meantime, however, spokesmen for Treasury Secretary Donald T. Regan said the administration will not oppose the indexing amendment and is, in fact, considering supporting it as part of the tax bill now before the House.

"We would have preferred it on a second tax bill," a Treasury official said, but he added that President Reagan will not fight the provision. Reagan has supported the concept of indexing the tax system to inflation -- in effect, annually reducing tax liability in direct proportion to increases in the inflation rate.

Gradison yesterday wrote Regan: "Based on our many conversations concerning my interest in including this legislation in the president's tax proposal, I now look forward in indexing not only being a part of the House Republican tax bill, but receiving the strong and active support of the president as well."

John Chapoton, assistant treasury secretary for tax policy, said a decision to add the indexing provision to the House bill depends on whether it gets the backing of the two key sponsors of the GOP measure, Reps. Barber B. Canable Jr. (R-N.Y.) and Kent Hance (D-Tex.).

Under the Senate bill, indexing would reduce tax revenues by $12.6 billion in 1985 and $37.4 billion in 1986, and would in effect establish permanent cuts to follow the 25 percent reductions in rate levels over three years called for in the administration proposal.

In other action in the Senate on the tax bill, backers of the president's three-year bill demonstrated their muscle by defeating the first Democratic challenge, 61 to 24.

The amendment, sponsored by Sen. Bill Bradley (D-N.J.), would have limited the personal tax cut to one year and targeted the reduction on people earning less than $50,000 a year.

The vote reflected the weakness of the liberal wing. Such senators as Edward M. Kennedy (D-Mass.) and Dale Bumpers (D-Ark.) argued futilely that the cuts should be skewed toward the level of the $21,00 median family income in the United States.

The Senate voted to lower the corporate income tax over two years in the lower brackets from 17 to 15 percent for income up to $25,000, and from 20 to 18 percent for income between $25,000 and $50,000. By voice vote, it approved an amendment to allow people whose spouses die or who are divorced to continue participation in tax-exempt retirement accounts initiated by the deceased or divorced spouse.