It's illegal if the intent is to deceive. Under S50(1) of the Police Act 1996:
Any person who with intent to deceive impersonates a member of a police force or special constable, or makes any statement or does any act calculated falsely to suggest that he is such a member or constable, shall be guilty of an offence and liable on summary conviction to imprisonment for a term not exceeding six months or to a fine not exceeding level 5 on the standard scale, or to both.
Their intent would need to be proven. It will be fact-specific; in some cases far easier to prove than in others. The criminal justice system is overburdened and underfunded so it is no surprise that these trolling videos are given no priority whatsoever.
Further complicating the matter is the need to correctly identify the individual to prosecute. Doing so would require a fair amount of police time, time that could perhaps be spent on more urgent priorities given the relative lack of harm these videos are doing compared to more serious crimes.
However, in this video (Would You Help a Police Officer Having An Asthma Attack?) an S50(2) offence would seem to have been committed by the actor wearing the police clothing:
Any person who, not being a constable, wears any article of police uniform in circumstances where it gives him an appearance so nearly resembling that of a member of a police force as to be calculated to deceive shall be guilty of an offence and liable on summary conviction to a fine not exceeding level 3 on the standard scale.
It does appear that both offences are being committed in these various videos, and the only reason people aren't being prosecuted is practical: there are more serious crimes to focus on, and the police would need to identify who exactly committed this crime--given these all happened at least two years ago, it would be challenging to say the least.
They also seem to commit the separate crime of wasting police time, for example by approaching cops in the street and falsely confessing to crimes.
Under S5(2) of the Criminal Law Act 1967, wasting police time is a criminal offence. Bringing proceedings in court requires the consent of the Director of Public Prosecutions (DPP) since those proceedings could have a chilling effect on the propensity of the public to report genuine matters to the police in the future.
It is likely that while "wasteful employment" of police time was caused by these people, so committing the offence, it is likely viewed simply as "part and parcel" of the job and the officer likely didn't spend any time at all investigating the confessions (depending on their nature).
Of course, even if the officer did spend time investigating the false confessions, the DPP would need to give their consent so unless the person has a demonstrated history of doing this (that would stand up in court) or the time wasted was of a particularly serious nature (e.g. the man who falsely claimed to be the Yorkshire Ripper), it seems unlikely consent would be granted.
