The number of housing starts stayed virtually flat from September to October, but building permits jumped sharply to their highest level since April 1981, the Commerce Department reported yesterday.

Another government indicator suggested that the recession deepened last month. The Federal Reserve Board reported that the nation's factories operated at only 68.4 percent of capacity in October, the lowest level in at least 35 years.

The 0.8 percent decline in factory use was the 13th in 15 months. The previous low was 69 percent in March, 1975, during another recession.

Building permits in October were up 18 percent from September and 60 percent from the severely depressed October 1981 rate, indicating that starts will rise in the months ahead.

Housing economists found the numbers encouraging and said it meant a turnaround in the industry had finally established itself.

But revised figures for September starts proved to be much lower than the original estimates, which had prompted President Reagan to proclaim a "rebound" in the industry and a beginning of economic recovery two weeks before the elections. The rise from August to September was only 7.6 percent, not 14.4 percent as originally estimated.

In October, starts were at an annual rate of 1.12 million, up only 1 percent from September's revised level of 1.11 million units but 31.4 percent higher than the 854,000 rate a year earlier. Permits were issued at an annual rate of 1.18 million in October, compared with 1 million in September and 738,000 a year earlier.

"Overall, its an excellent number," said Michael Sumichrast, chief economist of the National Association of Home Builders.

"It means a real recovery has finally started" for the housing industry, said Mark Riedy, executive vice president of the Mortgage Bankers Association.

While the starts figure stayed flat from September to October, this is not disappointing because permits have to be issued before starts can occur, Riedy said.

Starts in the Northeast in October actually declined by 35 percent from September, but permits rose by 20 percent. In all other regions, there was an increase both in starts and permits, with the South showing the most strength.