“Yesterday, I spent time at the C.F.P.B., I reviewed transition materials, and I met with members of Congress to lay out my plans for ensuring that the consumer bureau continues to fight for working families,” Ms. English said in a statement relayed through her lawyer, Deepak Gupta. “Today, I plan on spending the day at C.F.P.B. headquarters taking calls and meetings with external stakeholders and bureau staff.”

Judge Kelly, who was nominated by Mr. Trump and confirmed in September, had voiced issues at an earlier hearing on Monday, noting that lawyers for the president could not definitively say whether Ms. English was protected from losing her job. The judge also said that neither set of lawyers had addressed whether Mr. Mulvaney “can wear two hats.”

In a court filing, lawyers for Mr. Trump and Mr. Mulvaney said that the confusion surrounding the bureau’s leadership stems from Ms. English’s “meritless claims” because the president, the Justice Department’s Office of Legal Counsel and the agency’s general counsel all agree that Mulvaney is the acting director.

In a brief filed with the court, more than two dozen members of Congress — as well as former Representative Barney Frank, Democrat of Massachusetts — argued that the law clearly established Ms. English as the bureau’s acting director under Dodd-Frank, which was written to protect the agency from political influence.

Allowing the president to choose a successor under a different…

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