Around 21% more people die in winter than in summer in Kirklees, official figures show.
Experts say it is a "dangerous time" for elderly people, leading to persistent pressure on the NHS.
Every year, more people die in winter than in summer - due to colder temperatures, respiratory diseases and outbreaks of flu.
To measure the impact, the ONS compares the number of additional deaths between December and March to the rest of the year.
During the winter of 2016-17, the latest period figures are available, there were approximately 250 excess winter deaths in Kirklees.
This meant 21% more people died during winter in Kirklees, compared with the yearly average.
This was higher than in the previous year when there were 18% more deaths during winter.
According to the ONS, small population sizes can cause a significant amount of year-on-year variation at a local level.
Across Yorkshire and the Humber, winter was most deadly for people aged 85 and older.
Out of 3,910 excess winter deaths in Yorkshire and the Humber, 3,580 were older than 65, and 2,150 older than 85.
Across England and Wales, the rate of excess winter deaths varies from as low as 4% to as high as 51%.
Dr Nick Scriven, president of the Society for Acute Medicine, said that the data raised concerns "as to why there is such variation even between areas in a single region".
He said: "This data must act as a prompt to those in power to look at these trends and recognise that the capacity of the health service is being stretched beyond all measures in winter.
"We have an older, frailer population with increasingly complex medical problems, a lack of funding across health and social care to meet demand, a recruitment crisis and persistently poor performance."
Provisional data for England and Wales shows that excess winter deaths hit their highest level in more than 40 years during 2017-18.
There were an estimated 50,100 excess winter deaths, 45% higher than the previous year.
Health think tank, the King's Fund, said it was concerned that this "could be the start of a trend of periodically high winter deaths".
The Department of Health and Social Care said that the 2017-18 figures "were likely the result of a combination of flu and cold weather".
A spokesman said: "We know flu is difficult to predict - that's why this year we have a stronger vaccine for over-65s, and have made more vaccines available than ever before."