New sales figures from Sotheby Parke Bernet Inc. and Christie's auction houses show that the art market, which had suffered a recession, is climbing back up again.

The figures are especially interesting because of the dramatic fight for control of the international Sotheby's, which seems to have been won by American real estate developer Alfred Taubman.

According to Sotheby's, worldwide figures for Sept. 1, 1982, to Aug. 31, 1983, (actual sales figures from September to June, estimated figures for the few sales held in July and August) total 272,759,000 pounds sterling, which converts (at the current rate of $1.53 to the pound) to $417,321,270. Although the pound figure is up from 267,501,000 pounds in 1981-82, last year's dollar figure of $459,299,217 was higher because the average exchange rate then was $1.72 to the pound.

Graham Llewellyn, Sotheby's chief executive, said yesterday in London that worldwide profits (before taxes and "extraordinary items") will amount to more than 4 million pounds, in contrast to a loss the previous fiscal year of 3 million pounds. Llewellyn based the turnaround on increased confidence of consigners, higher sales prices, especially since January, and operating efficiencies.

Christie's is expected to release its worldwide figures in two weeks. Meanwhile, Christie's American sales were $141 million, 21 percent higher in the 1982-1983 season than last year. This was the best year since the London auction house opened in New York in 1977, according to David Bathurst, president of Christie's in America.