A House subcommittee controlled by Deocrats yesterday rejected some of the basic structural changes in unemployment insurance proposed by President Reagan to slash the program's costs.

But the subcommittee approved an important cost-cutting proposal by the administration in the government's main cash welfare progbram and appeared ready to accept Reagan's proposed "workfare" requirement to make welfare recipients work off part of their benefits.

It was the second area this week in which the president has been rebuffed by a legislative committee working on the nuts and bolts of his program, as opposed to the broad budget resolution now also progressing through Congress. The Senate Agriculture Committee and House subcommittees have been voting higher farm supports than Reagan proposed.

In Yesterday's action, the House Ways and Means subcommittee on public assistance killed, by a 6-to-5 party-line vote, a Reagan proposal to make persons receiving unemployment insurance take any available job at the minimum wage or lose their benefits after 13 weeks. Under existing law the states usually do not force an unemployed person to take much different from the one held previously.

The administration proposal was offered by W. Henson Moore (R-La.). Led by subcommittee Chairman Fortney H. (Pete) Stark (D-Calif.) six Democrats voted against the provision while four Republicans and Texas Democrat Kent Hance voted for the administration plan.

On an identical vote, a Hance amendment to eliminate the so-called "national trigger" for extra unemployment benefits was defeated. Under existing law, whenever the national unemployment rate for persons eligible for unemployment insurance is above 4.5 percent, jobless people in all states become eligible for an extra 13 weeks of benefits beyond the normal initial 26 weeks, even if unemployment in their own state is very low.

The administration proposal would make the extra 13 weeks available only in states which themselves have very high unemployment. Organized labor was strongly against both the Moore, and Hance amendments.

The subcommittee did go along with a Reagan proposal to change the way the national "insured unemployment" rates are calculated and thereby save about $560 million a year.

In the main administration victory yesterday the subcommittee adopted, 6 to 5, an administration plan to reduce substantially the amount of work income that can be ignored in calculating a household's welfare benefits.

Stark, in a document laying out Democratic alternatives to Reagan's proposals on a variety of welfare subjects, had proposed ceilings that saved only $49 million a year instead of triple that as Regan would. But L.A. (Skip) Bafalis (R-Fla.) countered with a slightly revised version of the administration plan and it was adopted when both Hance and Marty Russo (D-Ill.) voted with the Republicans.

Stark's "mark-up document" indicates that the subcommittee Democrats will resist many of the president's welfare proposals including reductions in social services, child welfare, foster care; his proposal to put into one block grant with a 25 percent cut a variety of social service programs; his proposals to put a gross income cap on welfare eligibility, to prohibit aid to strikers and to set up a national data bank on welfare recipients and make tax and other information from government files available to states.

But Stark would yield to Reagan on requiring all states to put in a "workfare" program. Stark's plan would achieve budget savings by taxing unemployment insurance benefits for higher income workers and thus make up for Reagan's higher income workers and thus make up for Reagan's proposed savings on the spending side that the Democrats don't favor.