Eleven environmental groups have banded together to counter the "destruction of environmental programs" they see in President Reagan's budget with a detailed budget proposal of their own.

"The president is using his budget to gut the environmental programs," said Larry Williams, lobbyist for the Sierra Club. "We feel that, given the searching that Congress is doing for alternate proposals, we need very much to put a better balance back into the environmental budget . . .keeping the administration from cutting EPA the Environmental Protection Agency in half, for example."

In the alternative budget released over the weekend, the groups claimed their spending plan would reduce the proposed $91 billion federal deficit by about $8.5 billion.

The plan would add $1.7 billion to 1983 budget authority for programs in energy, environment and transportation, and would use new taxes and fees on business to raise about $9.1 billion in extra revenues.

Budget specialists for congressional committees said that several of the proposals have a good chance of success, whether or not they are contained in an environmental package.

"There is a lot of feeling for put-ting back some money into EPA," said a senior staff member on the Republican side of a congressional committee. He said the proposals could also be a rallying point for environmentally minded congressmen.

"This budget is a philosophical alternative . . . . It gives members who are sympathetic a tool to work with," said Ken Murphy, staff director of the Environmental Study Conference.

The alternative budget would cut $290 million from nuclear programs and increase spending on energy conservation programs, such as tax breaks for insulating homes, by $650 million. Solar energy programs would go up by $200 million.

In the natural resources category, the environmental groups would cut spending in such areas as dam building by $600 million, and increase the EPA's pollution control programs by $1.7 billion.

The alternative budget would cut $1.8 billion from highway construction and put $1.5 billion into mass transit programs and $190 million into railroad support.

According to the Sierra Club's Williams, the two most important items in the proposal are the restoration of EPA's funds and the boost for energy conservation.

To balance the greater spending, the alternative budget proposes to gain $3.5 billion by eliminating the tax break that allows oil companies to write off labor, supply and testing costs incurred in exploring for oil.

Another $2 billion would be retrieved by collecting a 17 percent royalty from those who mine copper, gold, and other hard-rock minerals from federal land.

The groups sponsoring the budget package are the Environmental Policy Center, Friends of the Earth, the Izaak Walton League, the National Audubon Society, the National Parks and Conservation Association, the National Wildlife Federation, the Natural Resources Defense Council, the Preservation Action group, the Sierra Club, the Solar Lobby and the Wilderness Society.