The battle between Britain's labor unions and the Conservative government switched yesterday from the health workers to the coal miners, who rejected an improved pay offer and set the scene for a winter showdown.

As the miners threw down the gauntlet, union leaders met to consider further moves to push the pay claims of 600,000 health workers after Wednesday's nationwide strikes and protests.

Miners' leaders, demanding a 31 percent raise, dismissed as "wholly inadequate" what they said was a 7.2 percent offer from the state-run National Coal Board. The board said the offer was worth 8.2 percent.

The last confrontation with the 256,000 coal miners ended in a bitter national strike in the winter of 1973-74, which was instrumental in bringing down Conservative prime minister Edward Heath.

The National Union of Mineworkers executive decided to call a conference of delegates Oct. 4 to recommend rejecting the offer and holding a ballot to authorize strike action.

Pronouncing Wednesday's "day of action" in support of the health workers an overwhelming success, leaders of the 11 million-member Trades Union Congress called for more state hospitals to be reduced to emergency-only service and a series of regional strikes by health workers starting Oct. 4. They said the new protests were needed to "maximize pressure" on the government toward a favorable settlement of the health workers' pay dispute.