The doctors say the blame for the major issues should lie with NHS England and not hospitals and health workers.
The petition urges Parliament to pass a vote of no confidence in the chairman and board of the organisation, which sets NHS policies and direction.
It says: “It is clear that the current Board of NHS England does not possess the skills, wisdom or clarity of thought and purpose to continue to run and develop the NHS.
“Their continued presence threatens the future of our health and social care, and will affect all NHS users at some time.”
Yesterday it was revealed that a “large number” of hospitals, including in Leeds, are cancelling cancer operations due to a shortage of beds. That came after Prime Minister Theresa May said GP surgeries should open for longer to tackle the problems, which sparked an angry reaction from leaders in the field.
David Hutchinson, a retired consultant surgeon at hospitals in Leeds and Wakefield, is one of those behind the petition.
He said: “The present system can never succeed. The bed shortage is chronic and getting worse every year, and social care is even more underfunded.”
Sign at you.38degrees.org.uk/petitions/vote-of-no-confidence-in-nhs-england.
Meanwhile today the Parliamentary and Health Ombudsman was criticised in a new report which said a “significant number” of complainants receive a poor quality service.
* The Labour party in Leeds has organised a day of action next Saturday . Campaigners will gather across the city, including in Chapel Allerton, Oakwood, Halton, Meanwood, Burley Park and Hunslet, to demand emergency funding for the NHS.