It might be the case that there is no consultant available at any time on either day in some hospitals, although the report did not go into such a level of detail.
Having an admitting consultant is important because they can often assess the new patient better than a less senior doctor. In addition, they have the authority to ensure the best treatment is given.
The study also found that in nine out of 10 hospitals, consultants did not have to work 'blocks' of two or more days, but could chose to work a day here and a day there if they chose.
This was particularly the case at weekends, when one-on, one-off was a "recognised pattern of work".
The arrangement compromised patient care, concluded the report's authors, leading to "excess weekend mortality".
Dr Kevin Stewart, director of the RCP's clinical effectiveness unit, said "traditional rotas" with few consultants working weekends were putting lives at risk.
He said: "The profile of acute medical patients has changed dramatically over the past 20 years, yet in some hospitals changes in consultant working patterns have been much slower.
"Traditional rotas are neither safe for patients, nor good for clinicians."
He thought "substantially less" than four in 10 hospitals were acheiving the RCP's "gold standard" of having a consultant on the acute wards for at least 12 hours a day, every day, despite the growing clinical need for such a service.
"Now, patients are older, sicker and have more complex conditions, and they require dedicated consultants to be available on site 7 days per week for at least 12 hours a day," he said.
Death rates in large hospitals are lower than in smaller ones, according to the report, perhaps because those with fewer acute beds struggle to get good weekend cover.
The report also found that in half of hospitals, consultants only made one formal ward round per day.
The RCP calculated that one extra life could be saved per 443 acute patients, if consultants were made to work blocks of at least two days at a time, and carried out at least two wards rounds a day.
Elderly people make up the bulk of emergency hospital admissions.
Dr Simon Conroy, of the British Geriatrics Society, said: "We welcome the findings of the report, which emphasises the importance of getting frail older people seen at the earliest possible opportunity in their admission to maximise outcomes."
Dr Chris Roseveare, president of the Society for Acute Medicine, said: "This study represents a really important step forward in the management of patients admitted as medical emergencies.
"For the first time, specific patterns of consultant working on the Acute Medical Unit have been shown to be associated with improved patient outcomes; hospitals now have a fantastic opportunity to identify the number of acute medicine consultants required to deliver best practice and to provide sustainable rotas for 7 day working in acute medicine."
The study comes after Dr Mark Porter, chairman of the BMA's consultants' committee, called for members in acute departments to embrace weekend working.
*A network of 22 new major trauma centres that will save up to 600 lives a year are to be opened, the Health Secretary has announced.
Andrew Lansley said the network would mean more critically ill patients were taken to the right place first time, and would not have to be moved from one hospital to another.
He said: "For far too long, people have needlessly died from major trauma injuries because some local hospitals were not equipped with the right facilities or specialist teams to treat patients with life-threatening injuries quickly.
“I have always said that patients should be at the heart of the NHS and that services should be arranged around their needs, not how hospitals are organised. Seriously injured patients need to be assessed and treated quickly.
"With 22 new trauma centres now opening across England staffed with a full specialist trauma team, we hope to save up to 600 lives a year.”
The centres, in existing hospitals, will be equipped with "state of the art diagnostic and treatment facilities", added a Department of Health spokesman.
Professor Keith Willett, National Clinical Director for Trauma Care, said: “This new system is a great example of the difference that can be made to patients’ lives by having all the expertise, experience and equipment in one place.”