A Government review looked at infection rates and the impact on the NHS.
There were 104 patients admitted to hospital with Covid-19 in the last week and 632 people in hospital beds.
Julia Burrows, Director of Public Health for Barnsley Council, said: “Although we have seen the overall rate of infection reduce and start to level out across South Yorkshire over the past few weeks, we are now seeing signs that the overall rate is starting to increase again. This includes increasing infection rates in those over 65 years old.
“The pressure on NHS services also remains high, as they continue to try to provide routine health care on top of handling Covid-19 admissions. By moving out of very high restrictions at this time, we would put South Yorkshire’s hospitals at additional risk as well as the lives of vulnerable people.
“I understand this may be frustrating for many people, as so many have worked hard to reduce our rates. However, it is vital that we do all we can to keep the virus under control as much as possible as we have seen how quickly infections and deaths can increase.”
The South Yorkshire and Bassetlaw Integrated Care System Medical Director, Professor Des Breen, said: “The NHS is coping during this second wave of Covid-19, but we need everyone to help us contain the spread of the virus in the coming weeks to reduce the number of cases coming into hospitals.
“Recently, we had seen a steady decline in the number of cases but at the moment, we are seeing an increase in the numbers of patients with Covid-19 being admitted to hospital.
“The next few weeks are critical. If we start the New Year with the current numbers of patients in hospitals and see a further rise in cases following Christmas 'bubbles' at the same time as the usual winter impact on services, then this will put our NHS under severe strain.
“Our NHS Teams are working exceptionally hard to keep planned operations and care going and we now need you to help us, help you and your loved ones.”
He said: “Please take this virus seriously and play your part this festive season by limiting the chances of spreading the virus to others. Wash hands, wear a face covering, keep your distance from others. Think carefully about how best to apply the guidance on Christmas bubble to your circumstances.”
The new infection rate in all ages in South Yorkshire has ranged from 143 to 234 new cases per 100,000 people in the past seven days.
The new infection rate in over 60s was 161 new cases per 100,000.
The rate by which cases are rising and falling in South Yorkshire rate is between eight per cent and five per cent, when the Government wants it below five.
There is another tier review planned later this month.