Chris Hopson of NHS Providers had told media: "Too often, in too many places, standards of care are compromised and patients' safety put at risk".
Among those to have signed the letter are Ruchi Joshi, A&E GP at Walsall Healthcare NHS Trust, Ann-Marie Morris, consultant in emergency medicine at the University Hospitals of North Midlands, and Jo Taylor, from the Dudley Group NHS Foundation Trust.
This intervention comes as new figures show that just 66.5% of patients were treated within the four hour timeframe at major units in Lincolnshire in December 2017, well below the government target of 95%.
Health service: The BMA say there is a "growing gap" between patient demand and NHS supply.
The consultants draw on their own experiences - including patients dying prematurely, waiting times of 12 hours and more than 50 patients waiting for a hospital bed.
Dr Mann said the reason why some operations had been cancelled was to free up beds so "people are not waiting in corridors".
The consultants and heads in charge of the emergency departments of 68 acute hospitals wrote a letter to Prime Minister May stating the current state of the hospitals.
He added: "We are all proud of our NHS staff in enduring the conditions that have been created by Nicola Sturgeon, but is she really proud of what she has done to our NHS?" We are also keen to hear from patients.
Trish Murray, campaign manager at 38 Degrees, said: "Most people support an emergency cash injection for the NHS this winter and that's no surprise".
The higher flu rate in Scotland means the health service here is under greater pressure than the rest of the United Kingdom, she added.
"The hospital is extremely busy as would be expected during this winter period, and Trusts across the country are facing similar pressures".
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The facts remain however that the NHS is severely and chronically underfunded.
The letter states that the NHS has, "insufficient hospital and community beds and staff of all disciplines especially at the front door to cope with our ageing population's health needs".
As you will know a number of scientific publications have shown that crowded Emergency Departments are risky for patients. They have urged people to stay away from surgeries because there is no treatment. These departments are not outliers.
Bedford Hospital did not have a single unoccupied bed on two separate days during December, while one in eight ambulances had to wait for 30 minutes to drop off patients.
We have known for a number of years that recruitment of staff to Emergency Departments has been challenging.
The government was warned early last year that a winter fund was needed, but waited until the end of the year before coming up with any additional funding, which then proved to be too little too late.
The Gazette also reported yesterday how so-called bed-blocking - when patients are well enough to leave and want to do so but can not due to a lack of social care provision - is adding to the strain on hospital wards.
"And the number of elderly social care beds in England has actually gone up over five years and under her tenure they have gone down in Scotland". A number of independent organisations have confirmed that the United Kingdom has an inadequate acute bed base to meet the needs of its population.
Royal College and the relevant arms length bodies.
"While the pressure has not eased off since New Year's Eve, it is a testament to the hard work and dedication of our frontline staff that we have seen a reduction in ambulance handover delays".
You will understand with the public interest in this matter that we have released this letter to the press also.