A House subcommittee refused yesterday to adopt President Reagan's plan to meld a long list of social service programs for the poor and disabled into two "no strings" block grants to the states.

And the Senate education subcommittee voted to cut the maximum amount to government can spend on aid to education from $14.8 billion to $13.1 billion this fiscal year and $13.8 billion in fiscal 1982. But it made no decisions on how to apportion these cuts among programs.

Specifically, it made no decision on Reagan's proposal to blend most existing forms of aid to elementary and secondary schools into two block grants as well, nor on how to revise college student aid eligibility rules to shrink costs there.

These actions came as legislative units all over the Capitol began Phase Two of the budget process: the effort to make the specific program cuts required if Congress is now to stay within the broad spending totals proposed by Reagan and approved, with modifications, by a House-Senate conference on the budget yesterday.

In yesterday's legislative mark-ups, a Democratic strategy appeared to be emerging clearly: "protect the delivery systems."

That means making overall dollar cuts that Reagan has demanded, if unavoidable, but not necessarily according to his priorities. Instead, Democrats are trying to protect the programs they claim help society's poorest people and are rejecting many of his demands for giving states more discretion over federal money and for wiping out those laws ("delivery systems") that target aid to specific groups. That is one reason why his block grant proposals, giving governors near-total discretion on how to spend federal money, are, as Sen. Orrin Hatch (R-Utah) commented yesterday, "in some difficulty."

Here are some actions taken yesterday.

The House public assistance subcommittee on a final vote of 8 to 1 cut about $3.1 billion in fiscal 1982 from unemployment insurance, welfare, social services and children's aid programs. Reagan has sought $4.5 billion in cuts.

The subcommittee did approve Reagan's proposal to remove the "national trigger" that activates 13 extra weeks of unemployment benefits when joblessness is high. It also voted to tighten welfare eligibility rules and thus save about $700 million but this was $400 million less in welfare cuts than Reagan had wanted. It voted to allow but not require states to install "workfare" programs making welfare clients work off their benefits.

The subcommittee cut low-income energy assistance to $1.4 billion but refused to put it into a block grant as Reagan proposed. And it also refused to put social services, child welfare, foster-aid and adoption assistance into a block grant with a 25 percent cut. It declined to make unemployed people take any job at the minimum wage once they had been on the unemployment benefit rolls for 26 weeks.

The Ways and Means health subcommittee approved cuts totaling about $1.5 billion. It approved phasing out doctor "peer review" committees (PSROs) that help ride herd on hospital costs.

So far Ways and Means subcommittee have recommended the following cuts: public assistance, $3.1 billion; health, $1.5 billion; trade, $1.3 billion (chiefly by cutting trade adjustment assistance), and Social Security, $2.6 billion.