A United Mine Workers spokesman charged yesterday that Reagan administration budget cuts are reducing the number of federal mine inspections and reducing safety levels in coal mines. The charges were made in the wake of three coal mine accidents that killed 24 miners in just the past week.

"We just feel that the present attitude in the Reagan administration toward mine safety is not strong enough," Danny Davidson, the UMW deputy director for safety, said.

In its September budget proposal the Labor Department recommended eliminating 150 of 1,629 federal coal inspectors. But Ford B. Ford, assistant secretary of labor for mine safety and health, strongly defended the cutbacks. Ford said 72 inspections had been conducted in the past three years at the Topmost, Ky., mine in which eight were killed Monday.

"Generally, there may have been fewer inspections in the past year," Ford said, "but I just don't find a diminution of safety."

Meanwhile, attorneys for the Council of Southern Mountains, Inc., a citizens' group that includes Appalachian miners and their widows, asked the House Education and Labor Committee for a congressional investigation of the effect of the budget cuts on mine safety.

The attorneys charged the mine owners with a "pattern of violations" of mine-safety regulations that "show a need for more rather than less federal enforcement."

The three accidents appeared to have different causes. Although investigations still were under way, only the latest tragedy appeared to have been caused by a methane gas explosion, one of the more common risks in coal mine disasters.

Federal safety officials said workers at the Tennessee Consolidated Coal Co.'s mine near Palmer, Tenn., had just punched through the wall of an old shaft when an explosion rocked the mine Tuesday, killing 13. Investigators were attempting to determine yesterday whether methane gas had accumulated in the unused shaft, which had been closed for seven years.

At Topmost, where eight men were killed Monday after an explosion so violent it sent a shower of mud and water 300 yards out of the mouth of the mine, federal investigators were looking into the possibility that the miners accidently set off dynamite. Doctors said the men died of smoke inhalation.

Dr. George Nichols, Kentucky state medical examiner, said cigarettes and lighters were found on the bodies of three of the miners. "That is a distinct no-no in an underground mine," Nichols said. The doctor said there was no indication the lighters had been used but their presence "indicates things were pretty loose there, both with the workers and with management."

Last Thursday three miners were killed when rock and slate fell from the roof of a mine in Bergoo, W. Va.

The Tennessee accident was the worst in that state's history in 70 years. One of 17 survivors, who rode small rail cars to safety, said the mine started "shaking a little bit" and he "knew they had hit gas and it exploded." The miner declined to be identified.

John Parish, Tennessee Gov. Lamar Alexander's press secretary, said there was "strong evidence" the explosion was caused by methane. "But I don't think anybody is saying that officially."

Tennessee Consolidated operates 14 mines in the area. Federal investigators and the company president, William Allison, said the other mines would remain open.