Fox & Co., a national accounting firm, was charged yesterday by the Securities and Exchange Commission with "reckless" failure to detect false financial statements issued by three of its clients.

The first action against a major accounting firm in two years, the SEC complaint signals what is expected to be a significant number of such cases. An SEC spokesman said its inventory of cases of "cooking the books," or financial fraud, was increasing as corporations coming out of tough economic times seek to make their financial statements look better to prospective investors.

The SEC said in its complaint, filed in U.S. District Court in New York, that Fox, which has its headquarters in Denver and has 56 other offices around the country, knew or should have known that reports filed by Saxon Industries Inc., Flight Transportation Corp., and Alpex Computer Corp. were false or misleading. It asserted that if "Fox had not acted in such a reckless manner, it would have become aware of 'red flags' which indicated the possibility of irregularities."

Fox said yesterday it would contest the SEC's request for an injunction. "We refuse to be used as an instrument for possibly effecting a significant change in the disclosure obligations of auditors and of clients not involved in SEC action," said Fox Chairman Norman E. Klein.

Klein cited legal actions the SEC already has taken against the companies for "massive management fraud" in the "destruction, alteration and falsification of corporate books designed to deceive auditors, lenders, stockholders and even the SEC."

The SEC is asking the court to bar Fox from accepting any new clients until a committee has examined the firm's auditing procedures.

The complaint alleges that Fox "aided and abetted Saxon's material overstatements of revenues, net income and assets and understatements of liabilities." The 1981 statement included a write-off for $58 million in nonexistent inventory, the SEC said.

In the Flight Transportation case, the SEC charged that Fox failed to exercise due professional care by not performing substantive audits. The SEC said that Flight, a domestic air charter service located in Eden Prairie, Minn., overstated its 1980 revenues by $5.2 million, reporting a total of $8 million when its revenues allegedly were $2.8 million.

The SEC also accused Fox of aiding and abetting Alpex, of Boulder, Colo., in making allegedly fraudulent statements in connection with a stock sale to boost the company's balance sheet. As a result of the "sale," Alpex showed positive working capital of $525,000 instead of a negative $1.9 million, the SEC said.