Many people claimed that running a mile in less than four minutes would be impossible, nearly impossible or fatally dangerous.
One example of a scientist with very fine arguments in that tradition is as follows:
We have found an oxygen debt of 10 liters even after a quarter-mile in 55 seconds. It is obvious, therefore, that we can not pursue our argument below times of about 50 seconds, that the maximum speed is limited by quite other factors than the amount of energy available. It is not possible in any way to release energy explosively for very short intervals of effort: other factors determine the maximum speed, factors mechanical and nervous. Neither can the argument be applied to very long races, where-as we shall see below-other types of exhaustion set in.[…]
It is obvious that the 100 and the 220 yards (1/s mile) records are better than those lying in their neighborhood, that the quarter-mile record is extremely good, the 500 yards record very bad, by comparison with its neighbors. This
diagram should enable any enterprising and scientific athlete to select the records most easy to break: let him try those for 120 yards, for 500 yards, for three-quarter-mile, for three miles, but not for 220 yards, quarter-mile, one mile and six miles.
The degree, however, to which the body is able to run into debt for oxygen, to carry on not on present but on future supplies, is limited. When an oxygen
debt of about 15 liters has been incurred the body becomes incapable of further effort: it is completely fatigued.
Limits Of The Argument
It is obvious that we must not pursue the argument too far. A man can not exhaust himself completely in a 100 or a 200 yards race: even 300 yards is not sufficient to cause an extreme degree of exhaustion, though a quarter-mile, in the case of a first-class sprinter, is enough, or almost enough, to produce complete inability to make any immediate further effort.
("The Physiological Basis of Athletic Records"
A. V. Hill,
The Scientific Monthly,
Vol. 21, No. 4 (Oct., 1925), pp. 409-428)
Scientists using these numbers as a basis for detailed calculations look very precise:



With the data at our disposal, it should now be possible to arrive at some idea of the physiological limitations and capabilities of our subject. We have (a) a curve (fig. 2) of oxygen requirement per minute against speed, (b) information as to the subject's maximum oxygen intake per minute, and (c) some idea as to the maximum oxygen debt that he can incur. From these we can arrive at the figures of Table VI, which express the amount of energy of which the subject can possibly avail himself in various short intervals of time.
- […] The results obtained show the actual energy expenditure involved in the performance of the exercise, together with that involved in the " start" and in the "pull-up."
- It is shown that for the subject of these experiments to run 120 yards in 13 seconds necessitates an energy expenditure equivalent to an oxygen requirement of 29 litres per minute, or: to 13.7 horse-power. Attention is drawn to the extreme energy cost of rapid and vigorous exercise of short duration.
- An approximate means of allowing for the energy utilised in the "start" and in the "pull-up " is adopted, and the net oxygen requirement of running only is given in a curve as a function of the speed.
- The general relation between speed in running and oxygen requirement is as follows: The oxygen requirement per 120 yards increases about as the 2-8th power of the speed, whilst the oxygen requirement per minute increases approximately as the 3-8th power of the speed.
- The application of the physiological results to the calculation of the
optimum performance of the subject for any distance is described. The calculated optimum performances agree well with those actually recorded
(or estimated) by the subject, over the range 300 yards to 2 miles.
It is concluded that energy expenditure is the chief consideration in
determining athletic performances.
(R. M. Sargent: "The Relation between Oxygen Requirement and Speed in Running", Proceedings of the Royal Society of London. Series B, Containing Papers of a Biological Character, Vol. 100, No. 700 (Jun. 1, 1926), pp. 10-22.)
These calculations and graphs and arguments seem to prove that factors like energy expenditure, oxygen requirement and the related oxygen-debt incurred have limits that are approached asymptotically. That a minority of scientists and a majority of lay persons conclude from this an absolute value as scientifically proven is plausible.
But who really said the specific claim in question? One sports expert with a name:
Coach Brutus Hamilton, one of the most revered figures in track and field, published “The Ultimate of Human Effort,” listing the perfect records beyond which man could never go for the javelin, the shot put, the 100 meter, the 400 meter, the mile, the 5,000 meter, and the 10,000 meter. Hamilton backed up his analysis with detailed statistics, but many would have considered his word final even if he had jotted these “perfect records” down on a cocktail napkin. To the question, can the mile be run in four minutes flat? Hamilton replied, not quite. The fastest time that would ever be possible, he stated, was 4:01.6.[…]
And a concrete scientist, the same Hill from above, but more to the point and with a little more appeal to authority:
In 1927 British physiologist and Nobel laureate Archibald Hill wrote that “it’s not unusual for an athlete to tear a tendon, or to strain a muscle, and not unknown even for him to pull off a piece of a bone by an exceedingly violent effort. We are obviously not far from our limit of safety … athletics would become a highly dangerous pastime.”
(Both quotes selected from:
Neal Bascomb: "The Perfect Mile. Three athletes, one goal, and
less than four minutes to achieve it", Houghton Mifflin: New York, 2004.)
And of course, many of those quotes from the "doctors" and "scientists" are a nice fit for Clarke's First Law:
When a distinguished but elderly scientist states that something is possible, they are almost certainly right. When they state that something is impossible, they are very probably wrong.
From a historical viewpoint:
The First 4-Minute Mile, 60 Years Ago
For more than a decade the world record for the mile had remained stuck at 4:01. Many thought it unbreakable, and dozens of medical journals reported that it was physiologically impossible for the human body to break through the barrier. Sixty years ago, however, a British medical student proved them wrong.
More background on the science, or better: explanation, for why the record would stand comparatively long:
But it was still a breakthrough, right? He still showed people what was possible. I mean he broke a world record that was on the books for 9 years! And after he broke it, the mile was taken to another level. Herb Elliott dropped the record down to 3:54.5 within 4 years! Surely, a psychological breakthrough was the key!
It makes for a compelling narrative, one that is thrown around at success seminars left and right, meant to inspire you to let go of your psychological barriers. But is it true, did Bannister usher in a new era? […]
And there it stayed until Bannister broke it 9 years later. Why the stagnation?
The obvious answer is, it was 1945 and we had just completed that little thing called World War 2. You see, during the war years, the Swedes (Anderson and Hagg) had the freedom to continue their athletic careers, chasing records, while the rest of the world, for the most part, was put on hold. Not only that, but we lost scores of top talent to deaths and injuries during the war. For a popularized example, see Unbroken hero Louis Zamperini. So not only were we hurt athletically during the war, but also during the post war era.
Additionally, while Hagg and Anderson were taking their shots, in 1946, they were banned from competing as they were labeled professionals for taking money, which was against the amateur rules of the day. At the ripe age of 27, less than a year after he ran 4:01.4, Hagg’s career was finished.
Conclusion:
To balance it out:
There are really two answers to this one.
Yes, it WAS considered impossible – by the general public who were being fed the line constantly by sportswriters. And yes, there were scientists who proclaimed that it was impossible. But there were scientists who said that it WAS possible.
In the sport itself, though, it was deemed a sheer inevitability.
Going by this absolute from the OP headline: there were some doctors and other scientists saying that it would not be possible or very dangerous to even try. But "that the scientific community at the time deemed the feat impossible" seems unlikely:
The tendency for journalists to drum up conflict and drama easily explains why the “barrier” was created. It also explains why so many doctors were quoted saying it was dangerous. Danger sells papers. Bannister himself was a medical student at the time he broke the barrier, trained in the same medical system as the rest of the doctors. It is highly unlikely that he was unique in his beliefs.