Public Health England data compares the number of deaths registered with how many were predicted based on previous mortality rates to calculate the number of excess deaths in an area.
Based on estimates for 2015-19, Sheffield was predicted to see 5,016 deaths from any cause in 2021, but 5,203 were recorded last year – 187 (4 per cent) more.
Of the deaths registered last year, 632 (12 per cent) had Covid-19 on the death certificate.
In 2020, there were 810 excess deaths in the area – though figures for that year only began at the end of March.
Excess deaths are considered a better measure of the overall impact of Covid-19 than simply looking at mortality directly linked to the virus, as they capture deaths that may have been indirectly caused by the crisis.
Since March 2020, 115,600 excess deaths have been recorded across England, causing a greater fall in life expectancy than anything seen since the Second World War, according to the King’s Fund.
However, last year saw a total of 43,300 excess deaths, which was down from 72,300 in 2020.
Veena Raleigh, senior fellow at the think tank, said: “Covid-19 has struck in waves, and its future course is uncertain.
"However, although the pandemic has taken a toll of life that is unprecedented in recent years, the signs are that it is abating.
"Many factors will have contributed to this – the vaccination programme in particular."
She added that some areas have suffered a greater loss of life than others, which is reflective of the "disproportionate impact" of coronavirus on deprived areas and people from ethnic minority groups.
North Somerset, in the South West, saw fewer deaths in 2021 than were expected – the only part of the country to do so.
Meanwhile, the London borough of Newham recorded 28 per cent more.
The Nuffield Trust said lockdown measures reduced the circulation of flu and other illnesses, which could be why the number of excess deaths nationally was lower than the number of Covid deaths in 2021.
And Sarah Scobie, deputy director of research at the organisation, said that some patients who died from Covid may have subsequently died from a different cause instead if they had survived.
She added: "As the vaccination programme has rolled out, the number of Covid deaths has reduced, despite high numbers of cases.
"The huge toll of Covid should not be underestimated though – there have still been hundreds of excess deaths recorded every week since July 3 2021.”
The deadliest time of the year in England came over three weeks in January and February when there were around 5,000 excess deaths each week.
But in Sheffield, the highest weekly excess death total came in the seven days leading up to August 13 when the area recorded 62 excess deaths.
By contrast, there were 54 fewer deaths in the week ending April 16 than had been predicted.