Because the regular policemen that a criminal meets are not armed, a criminal caught committing an illegal act will not fear his (or her) life is in immediate danger, so there is no need to start shooting, or even, (as others have pointed out), carry a gun in the first place. Therefore, they can try to run away in safety.
Because of this, very few policemen get murdered on the job. According to statistics it averages about 2 policemen unlawfully killed every 3 years in the UK.
Because the murder of police is so rare, whenever it happens it becomes front page news until the criminal is caught. It is the crime with the highest clear-up rate – consider it a 99.9% chance of being caught.
Therefore, an armed criminal, confronted by an unarmed UK policeman has two options:
- to run away, or,
- to shoot the policeman.
Going for the first option has some chance of escaping justice, and a worst case of a prison sentence proportionate to the crime. Going for the second option means they are guaranteed getting a life sentence. Therefore, only very stupid, (and/or foreign), criminals shoot at the police.
Because of this, carrying a gun gets even rarer among criminals, they are even more likely to run away rather than stay and fight, and we’re back at step one.