A subject living under common law in the UK is liable for punishment for not acting to quell a disturbance: this is the considered legal opinion of A.V. Dicey, one of the foremost British jurists.
According to Dicey, there is no essential difference in the common law between a subject and someone like a policeman, whom it is thought, has a special power to deal with public disorder.
If a policeman heard of a disturbance somewhere and decided to continue eating doughnuts or Doritos (or do some very important paperwork which I’m sure is more usual!!) they would be liable.
However, a policeman enjoys no exalted position in common law over a mere subject. This negligence is not confined to police, as Dicey tells us:
The Crown has the right to put down breaches of the peace. Every subject, whether a civilian or a soldier, whether what is called a “servant of the government,” such for example as a policeman, or a person in no way connected with the administration, not only has the right, but is, as a matter of legal duty …bound to assist in putting down breaches of the peace. (Introduction to the Study of the Law of the Constitution, p. 284)