The segment of the video I watched is wrong or misleading in several ways.
The speaker apparently claimed to be performing a "citizen's arrest" on a police officer on the basis of s.5 of the Public Order Act 1986. The question above also talks about s.26 of the Criminal Justice and Courts Act 2013, which deals with an offence of improperly exercising the powers of a constable.
Somebody who is not a police officer is allowed to arrest somebody else without a warrant only under tightly defined circumstances. These are given in s.24A of the Police and Criminal Evidence Act 1984 (inserted by the Serious Organised Crime and Police Act 2005). The elements include that the offence be indictable, which does not mean as claimed in the video that "you can get sent to prison for it", but refers to the mode of trial. Some summary offences are imprisonable. Since the offence under s.5 of the 1986 Act is a summary one, rather than indictable, we fall at the first hurdle.
A further qualifiction is that this power of arrest can only be exercised if the person believes it would be impractical for a constable to do it instead, and that the arrest is necessary to stop the arrestee from escaping, hurting themselves or someone else, or damaging property. In the video, the police officer does not look like he is doing any of those things, and there is another officer right next to him. Thus it would be hard to argue that there are reasonable grounds for arresting the officer in this way.
Also, while members of the public may object to the conduct of police officers, that does not always amount to an offence under s.26 of the 2013 Act. The offence there is about corruption, exercising the powers of a constable for personal benefit. That personal element does not seem to be shown in the video.
There are some other mistakes in the part I watched.
- A lawful arrest cannot be effected just by using the words "I am arresting you". The arrestor has to take or imply some directive action as well, or else there is no arrest at all: just two people continuing to stand awkwardly. This also goes to the point about needing to stop the arrestee from causing injury (etc.) - if you aren't actually taking steps to restrain them then you can't say you're preventing the harm. The point of the provision is to take the fact of an arrest (I am stopping you from getting away) and make it a legal arrest; it can't conjure up an arrest where none exists.
- In a citizen's arrest there is no need to give a warning about "anything you say may be used against you" or whatever. This is applicable to the police when they are questioning suspects, which is not what is happening here. Indeed, while the police can arrest somebody without warrant because they want to investigate whether they've committed a crime, a regular person can't.
- Although there is a statutory requirement to tell somebody why they've been arrested, coming from ECHR as well as domestic common-law principles, the police are not expected to cite the law with precision. It's OK to say "I'm arresting you for selling heroin" rather than "I am arresting you because I have reasonable grounds to suspect you of supplying a controlled substance to another without lawful authorisation, contrary to section 7 of the Misuse of Drugs Act 1971". While there are more rules that kick in during pre-charge detention or questioning, the law recognizes that the operational circumstances of an arrest make a briefer explanation more appropriate. Indeed, more formal language would defeat the point of the rule, which is that the arrestee should know what's going on.
- "You can only arrest a cop for an indictable offence" is not quite right. You (a non-constable) can only lawfully arrest anyone for such an offence, and if the other conditions are met. A constable can be arrested for any kind of offence: there's no special immunity for summary offences.
As to the general question of "How can one arrest a police officer?", the usual way is to become a police officer yourself. Almost all arrests, especially those involving police misconduct, are done by the police. For corruption it is likely that an arrest would be made after a long investigation and after the issue of a warrant, rather than on the spur of the moment.
As a normal person, wilfully obstructing a police officer in the execution of his duty is an offence (Police Act 1996, s.89), and affecting an arrest may amount to assault on the officer. That does not make it impossible to arrest an officer in this way, just fraught with future difficulty.