More than 1,500 housing-related organizations across the country have sent a letter of protest to President Reagan over proposed funding cuts for housing assistance for the poor, saying the reductions would have "grave consequenses for thousands of low-income households already in grave circumstances."

The letter was signed by Edward Brooke, former U.S. senator from Massachusetts and chairperson of the National Low-Income Housing Coalition as well as a member of the President's Commission on Housing. It was hand delivered to the White House Thursday, just before Housing and Urban Development Secretary Samuel Pierce made his direct budget appeals to the president.

Meanwhile, sources said Reagan has agreed to continue funding in fiscal 1983 for urban development action grants (UDAG) at the fiscal 1982 level of $458 million, once again overturning budget office attempts to kill the program. UDAG provides grants to deteriorating cities to encourage private investment and economic development in blighted areas.

Originally 85 national and 997 state and local groups signed the letter, and several hundred more signatures endorsing it are being sent separately to the White House. The list of signers includes a wide variety of housing authorities, representatives of civil rights groups, unions, church organizations, day-care centers, civic associations, and senior citizens groups.