LONDON — In a land where matters of public health care are never far from scrutiny and sometimes scandal, the British medical authorities acknowledged on Monday that they were checking the credentials of some 3,000 foreign physicians after one was convicted of fraud and accused of falsifying qualifications.

The case could add to concerns about the safety of patients in Britain’s once-vaunted National Health Service, even as tight budgets and the possible impact of Britain’s pending departure from the European Union have augmented a sense of unease.

For more than two decades, Zholia Alemi, 56, worked at health facilities in Britain using what she said was a qualification from her native New Zealand. The document enabled her to treat patients suffering from dementia and an array of other psychiatric complaints.

But in recent weeks, an investigation by a provincial newspaper uncovered a very different version of Ms. Alemi’s background.