A strong surge in consumer spending pushed up profits sharply for two local retailing companies, according to earnings reports issued yesterday by Woodward & Lothrop Inc. and Scotts Seaboard Corp., the parent company of Scott's Home & Garden Centers.

Woodward & Lothrop earnings increased by almost 125 percent in the second quarter that ended July 30, to $2.387 million (64 cents a share), from $1.062 million (28 cents) last year.

Sales for the latest quarter totaled $90.3 million, an increase of 15.3 percent over sales of $78.3 million for the same quarter in 1982.

For the first six months of the year, Woodies' earnings increased 148 percent over the 1982 period, to $3.1 million (84 cents) from $1.3 million (33 cents), even though revenues were up only 13.7 percent, from $153.6 million to $174.6 million.

Edwin K. Hoffman, Woodies' chairman, attributed the sharp increase in revenues to strong consumer spending in the Washington metropolitan area. "The strong sales performance for the quarter and good expense control enabled us to significantly improve our profit performance for the quarter and six months," he said.

The company also benefited from a $1.14 million reduction in interest expense as a result of significantly reduced short-term borrowing and lower interest rates.

Meanwhile, Scotts announced record profits of $1,001,000 (55 cents) for the quarter that ended July 30, compared with net income of $80,000 (4 cents) for the same period last year.

Sales for the quarter totaled $10.6 million, up 27 percent from $8.3 million in last year's quarter.

For the first six months of the year, Scotts had profits of $1.16 million (64 cents), compared with a loss of $366,000 (19 cents) for the first half of 1982. Sales rose from $15 million to $18.8 million.