By Allie Malloy, CNN

(CNN) -- A showdown over the leadership of a major consumer fraud protection agency was underway Monday morning, as both President Donald Trump's pick to lead the Consumer Financial Protection Bureau and the person tapped by its former director showed up to work.

Sunday night, lawyers for Leandra English, whom Richard Cordray named the effective acting director when he resigned on Friday, filed a lawsuit in the US District Court for the District of Columbia seeking to halt the appointment of Mick Mulvaney, who serves as head of the Office of Management and Budget and is also named in the lawsuit.

Both Mulvaney and English were present at the CFBP Monday morning. Mulvaney was given full access to the CFPB director's office with "full cooperation" from its staff, a senior White House official told CNN, adding that the OMB director brought doughnuts for his new staff. English, according to a source familiar with the matter, also was present at the bureau Monday morning, but it was not immediately clear if she and Mulvaney interacted. Mulvaney's communications director tweeted a photo of his boss "hard at work" in his new position.

English's move marked a stunning turn of events at the agency, which was created after the financial crisis to protect consumers and keep an eye on Wall Street. While serving in Congress, Mulvaney voted in favor of killing the bureau, arguing it has too much power and issues unduly harsh regulations, and he has worked alongside Trump to roll back some of the agency's rules.

In his exit letter, Cordray said the consumer agency's work is vital to the US economy, and proponents, such as Massachusetts Democratic Sen. Elizabeth Warren, say it plays a key role in preventing big business from preying on the little guy.

English said in a statement Sunday: "The talented, dedicated, and hard-working staff of the CFPB spend every day standing up for consumers. As acting director, I am filing this suit to stand up for the CFPB."

In their court filing, attorneys for English argue she is entitled to the position under the Dodd-Frank Wall Street reform law, which created the agency and says the deputy director becomes acting director when the agency's top spot is vacant. When Cordray resigned, he named English, then his chief of staff, as deputy director, establishing her as the bureau's acting director.

But Trump named Mulvaney the head of the agency shortly after Cordray appointed English, signaling a potential showdown over who will take charge of the federal watchdog agency.

"The President's attempt to install a White House official at the head of independent agency — while allowing that officer to simultaneously serve in the White House — is unprecedented," said English's lawyer, Deepak Gupta of the law firm Gupta Wessler, in the statement on Sunday. "The law is clear: Ms. English is acting director of the Consumer Financial Protection Bureau until the Senate confirms a new director."

The White House defended their decision Sunday night despite English's court filing.

"The administration is aware of the suit filed this evening by Deputy Director English. However the law is clear: Director Mulvaney is the Acting Director of the CFPB," said White House press secretary Sarah Sanders in a statement. "Now that the CFPB's own General Counsel -- who was hired under Richard Cordray -- has notified the Bureau's leadership that she agrees with the Administration's and DOJ's reading of the law, there should be no question that Director Mulvaney is the Acting Director. It is unfortunate that Mr. Cordray decided to put his political ambition above the interests of consumers with this stunt."

On Saturday morning, the White House defended Trump's choice of Mulvaney as the consumer agency's acting director, calling it a "typical, routine move."

Mulvaney and his team were not expecting a showdown at the agency Monday morning, a source close to the OMB director told CNN. They view Mulvaney's appointment as something that the Justice Department, consumer agency lawyers and staff agree upon and expect a normal transition, the source said.

Arkansas Sen. Tom Cotton, a member of the Banking Committee and longtime critic of the Consumer Financial Protection Bureau, called English's lawsuit "just the latest lawless action" by the agency, which he labeled "rogue" and "unconstitutional" in a statement Sunday night.

"The President should fire her immediately and anyone who disobeys Director Mulvaney's orders should also be fired summarily," Cotton said. "The Constitution and the law must prevail against the supposed resistance."

But Sen. Dick Durbin, D-Illinois, said on CNN's "State of the Union" Sunday that the White House's move was intentionally aimed at dismantling the agency.

"Wall Street hates it like the devil hates holy water. And they're trying to put an end to it with Mr. Mulvaney stepping into Cordray's spot," he said. "But the statute is specific, it's clear, and it says that the deputy shall take over."