Giving to United Way nationwide has risen nearly 24 percent in real dollars since 1981, from $1.6 billion to last year's $2.6 billion, says Edward A. Brennan, United Way of America volunteer chairman.

Brennan reported last week to President Reagan that the economic improvements of the past seven years - an increase in employment, decrease in inflation and increase in discretionary income - have contributed to United Way's success.But much more remains to be done for people who have not fully shared in the economic recovery, he said, so United Ways around the country have committed to doubling their volunteer and financial resources through their "Second Century Initiative."

Mark Miller, president of Mark Miller Subaru and Mark Miller Pontiac, Salt Lake City, and his wife, Kathie, were among a group of United Way local leaders who accompanied Brennan to the White House for the report.