I think there are many reasons why the police did not catch Jack the Ripper, even though at one time they believed that they were only five minutes behind him after the murder of Catherine Eddowes on 30 September 1888, the night of the double event.
One reason was that policing in those days was far removed from the efficient methods of today. Just imagine no fingerprinting until 1906, no crime scene analysis, no DNA, no genetic sequencing, or any of the other tools that the police now have.
On top of that you must remember that the area was dimly lit with gas lighting mainly on the larger thoroughfares with little, if none in the small streets, alleys and courts. In fact, due to the murders, Queen Victoria ordered that every court should be lit.
There were many people on the street days and night due to the large percentage of homeless people in the area (a fact which has sadly not altered much today, it seems to be a magnet for the destitute). Although this was true, many of these people were alcoholics and Jack murdered in the early hours of the morning when most would have been overcome with drink and sleeping it off, until they were moved on by the police or arrested. Even if they were awake would they, in their drunken condition notice a bloodstained man? Blood stains hardly show on black clothing at night even today unless you are somewhere well lit, so back then they probably would not have shown at all.
Furthermore, there were many slaughterhouses in the area which were operational in the early hours, just as they are today. Imagine if Jack had on a butchers/slaughter man’s apron stained in blood would anyone have taken any notice given that it would have been a common sight?
As a last point I must say that the investigation was hampered by the fact that the Metropolitan Police and the City of London forces did not communicate or pass information to each other. This is shown on the night of the double event when Catherine Eddowes was murdered inside the boundary of the City of London. The City police who discovered her body in Mitre Square rushed on what they believed to be the trail of Jack the Ripper into the Metropolitan area eager to catch Jack and outdo the Metropolitan force.
With all these problems for the investigation by the police it is not surprising they did not catch him.
