It comes as the number of infections in the Black Country rose by 3,000 in seven days – or 41 per cent.
The plea has been made by doctors at Russells Hall Hospital in Dudley and Wolverhampton’s New Cross Hospital, in Wolverhampton.
There are now almost 300 Covid patients at New Cross, forcing it to expand the intensive care ward. Similar pressures are being experienced at all hospitals in the West Midlands and Staffordshire.
Dr David Stanley, pictured, a consultant intensivist who works in critical care at Russells Hall Hospital, said: “At the moment, this is an absolutely crucial time. We know that from the way the numbers are rising. Please stay at home and follow the rules.”
In October, the number of Covid patients attending Russells Hall Hospital began “picking up” from lesser numbers, said Dr Stanley.
But since Christmas, he says patient numbers have “gone up significantly”.
“We have become much more stretched in terms of the staffing the facilities,” he said.
Asked if West Midland hospitals could follow the lead of hospitals in London, Dr Stanley said: “Yes, we will have to prioritise our work. We will have to concentrate on emergency and urgent work because of the pressure.
"Essentially, all those Covid patients are a new group, on top of our normal work. That has been the big challenge for the hospital and everywhere in the country.”
Dr Brian McKaig, deputy chief medical officer at the Royal Wolverhampton NHS Trust, which runs New Cross, added: “It is exceptionally busy at New Cross Hospital.
"We have got our job to do here in the hospital. We need the general public to do their job too.”
Data provided by the Government shows that in the last seven days, there has been 10,400 new Covid cases in the Black Country. This rose from 7,336 the week before.
Wolverhampton currently has the highest infection rate in the Black Country, with 1,018 cases per 100,000 people.
Sandwell has the second highest infection rate in the Black Country, with 971.2 cases, while Walsall is in third with 791.7, and Dudley is in fourth with 705.9.
In the West Midlands, the number of cases rose by 39 per cent over the last seven days, from 26,424 to 36,753.
This move will also see elective surgery, which is non-emergency, stood down to avoid being overwhelmed. UHB NHS Trust is currently caring for 125 Covid-positive patients.
Dudley has seen a 36 per cent increase in Covid cases over a week, rising from 1,665 to 2,270. It follows a national trend of rising cases, which has seen some non-emergency care postponed in London hospitals by the NHS.