The controversy that President Reagan had hoped to quell with the resignation of Environmental Protection Agency Administrator Anne M. Burford showed no signs of abating yesterday.

Congressional Democrats announced they would continue to press their investigations and critics renewed calls for a complete policy change at the EPA. In addition, speculation grew over who will be named to replace Burford and what qualifications that person will need to be acceptable to the Reagan administration, to Congress and to environmental groups.

"The departure of Burford does not mean there's any change in the policies," said Rep. John D. Dingell (D-Mich.), chairman of a House Energy and Commerce subcommittee that yesterday received four boxes of documents it had subpoenaed for its inquiry into the EPA. The White House agreed to turn over the documents just before Burford resigned, heading off a possible second contempt-of-Congress case against her.

"Mrs. Burford is being denounced for doing exactly what the administration told her," Dingell said. "This administration's priorities have got to change, I would say 180 degrees."

The White House showed little inclination to move quickly to name a permanent successor to Burford, who resigned Wednesday. Presidential aides indicated they wanted to give the acting EPA administrator, John W. Hernandez Jr., and a new team of managers named by the White House two weeks ago time to bring new order to the agency.

Hernandez, who was Burford's deputy and has let it be known he would like the top job permanently, told reporters he intended to "begin immediately the task of restoring the public's faith" in the embattled agency. My No. 1 priority is to get this agency back to work."

But several congressional subcommittee chairmen said they would continue to examine allegations of mismanagement, conflicts of interest and political manipulation at EPA, and whether they lead to the White House.

"Don't let anyone tell you the White House didn't control what was going on at EPA," Dingell said. "We're looking at whether political judgments on toxic waste cleanup went higher than EPA."

Leading members of Congress, environmentalists and some EPA officials said yesterday they expect the choice of a new administrator to indicate how the White House is reacting to the controversy over its environmental policies. A senior EPA official said the agency needed a "world-class person, who can immediately develop credibility."

In a television interview, Sen. John H. Chafee (R-R.I.) said, "It is my hope Reagan will place in charge of the agency someone who . . . carries with him strong environmental credentials, a good administrator . . . someone who is truly dedicated to these programs."

Rep. James J. Florio (D-N.J.) said that the White House "has put a tourniquet around their political wound, but if they appoint a Burford clone or someone who reflects the same mentality, then we've gotten virtually nowhere. I don't think you're going to convert any people in the White House into Sierra Club members, but they are not totally obtuse to the political implications of this."

Sierra Club President Denny Shaffer urged Reagan to appoint an administrator free of ties to the industries that the EPA is charged with regulating, and to back that person with a strong new financial commitment to environmental programs.

Administration officials had earlier floated the name of John R. Quarles, a Washington attorney who served as deputy EPA administrator in the 1970s. But the White House has been warned that Quarles would be unacceptable to Sen. Robert T. Stafford (R-Vt.), chairman of the Senate Environment and Public Works Committee.

Because Quarles has represented industry on the Clean Air Act for the last two years, as the director of a lobbying group comprising more than a dozen major oil, paper, chemical and automobile corporations, he likely would be required to recuse himself from any EPA business involving the Clean Air Act or those corporations. According to Senate aides, he aslo earned the enmity of Stafford by characterizing him in a newsletter as an "environmental extrmeist."

Stafford said yesterday that the appointment of Quarles "would mean business as usual at EPZ."

Other names suggested as candidates for the vacancy at the EPA range from Donald Kennedy, a Democrat who was Food and Drug Administration chief under the Carter administration and is now president of Stanford University, to Millicent Fenwick, the New Jersey Republican defeated in her Senate bid last year.

Many of the names are familiar from two years ago, when the White House spent months sorting through candidates for the EPA before selecting Burford, then named Anne M. Gorsuch. Among them are James R. Mahoney, founder of a Massachusetts consulting firm that caters to industrial clients; Henry L. Diamond, a Washington attorney and former New York state natural resources commissioner, and Stanley W. Legro, a Californian and an EPA enforcement official under President Nixon.

But the speculation also included new names, among them Carol E. Dinkins, assistant attorney general for land and natural resources, and Patrick Raher, a Washington arrorney who has handled regulatory matters and lawsuits for both environmental and industry clients. They both said they had not been contacted by the White House.

Another potential candidate is Charles R. Ross, a former official of the Federal Power Commission who is now a private attorney in Vermont. He is popular amoung conservationists for his strong pro-consumer philosophy.

Some congressional and environmental critics of the agency said a change in policy would require more extensive administrative changes. "They are going to have to clean house over there," said on Senate aide.

In a briefing for senior EPA staff members yesterday afternoon, Hernandez did not indicate he would make any personnel changes. But EPA employes at all levels said they expected some people to go eventually. "A new administrator will want to put his or her own people in place," said one senior official.

The EPA already has hired a new public affairs director, William J. Ahlfeld, a vice president of the American Forest Institute.

Ahlfeld sought to generate some positive news yesterday by disclosing that Hernandez expects to announce next week a proposed compromise agreement that would give 111 counties that are violating the Clean Air Act more time to avoid federal sanctions.