Hundreds of patients "gave up" and left A&E without being assessed last year at the Calderdale and Huddersfield NHS Foundation Trust, figures show.
A leading expert has expressed concern that hundreds of thousands of patients across England may be coming to harm as a result of leaving hospital prematurely.
Patients who attend A&E are assigned an outcome based on how their visit ended – for instance, whether they were admitted, referred to a specific clinic, or died.
NHS Digital figures show that 504 patients were recorded as having left A&E without being seen by medical staff at the Calderdale and Huddersfield NHS Foundation Trust in the 12 months to May .
They joined 308,500 others across England who also left hospital before being assessed or treated.
Dr Nick Scriven, president of the Society for Acute Medicine, said it was a "major concern to see so many people essentially giving up and leaving".
He added: "The optimistic version is that these people probably did not need emergency care and, when faced with the reality of a long wait, reconsidered.
"The alternative is that they were in need but potentially could have come to harm by leaving unseen."
The number of people who leave without being seen is one of five quality measures used to monitor the performance of A&E departments each month.
During May, the latest month with available data, 1.9 per cent of patients across England left without being seen.
This was an improvement on the same month two years ago, when it was 3.3 per cent.
However, the figures exclude patients who have an unknown outcome, because staff did not record it.
Of the 1.7 million people who attended an A&E department in England in May, 13 per cent had an unknown outcome – up from just one per cent in 2017.
At the Calderdale and Huddersfield NHS Foundation Trust, less than one per cent of patients did not have an outcome recorded for them during May.
Dr Scriven said it was concerning to not know what outcomes so many patients had faced.
An NHS spokesman said the proportion of patients leaving without being seen had improved in recent years, despite an increase in an increase in visits to A&E.
He added: "This improvement comes as more people than ever are making use of the NHS 111 phone and online service, which has prevented more than 12 million unnecessary trips to A&E since 2011, by providing people with fast and free advice on more appropriate and convenient options."