Embassy spokeswoman Lynne Platt said Lawson was stopped from traveling Sunday and had subsequently been invited to the embassy to apply for a visa.
A spokesperson for U.S. Customs and Border Protection would not comment directly about Lawson's case, but told CBS News in a statement, "Applicants for admission bear the burden of proof to establish that they are clearly eligible to enter the United States. In order to demonstrate that they are admissible, the applicant must overcome all grounds of inadmissibility."
Lawson admitted that she has taken cocaine a handful of times while testifying at a trial in December involving her two former assistants, who were accused defrauding her and her ex-husband, Charles Saatchi.
She tweeted Saturday that she was going on vacation, but she also has worked in the U.S., where she co-hosted TV cooking competition "The Taste."
British citizens need visas to work in the U.S. but not for a vacation. U.S. authorities may refuse passengers admission for various reasons, including drug use.