Actually, your advice is pretty lousy too and presumably "gathered by Googling." What should happen and what actually happens is not necessarily the same.
The numbers of prosecutions for domestic violence relative to the number of complaints is tiny. This does suggest the police find it quite challenging to go from the point they receive a complaint to the point that they can persuade the CPS to take the prosecution forward. The numbers of prosecution for coercive control is even smaller.
That's not to say that it's a bad idea to go to the police but rather that I wouldn't have a huge degree of confidence that the complaint would progress very far without evidence. The police cannot prosecute someone solely on the word of a victim and the CPS will want to be reasonably confident that the perpetrator will be found guilty "beyond reasonable doubt" (and unlike domestic violence, they cannot even take photograph evidence that a person has been subject to violence by someone).
Two particular challenges in proving coercive control are first that the examples of behaviour, if isolated rather than "repeated" and "consistent," can be reasonable (e.g. a number of people on this forum have taken it upon themselves to surveil a husband they think is guilty of having an affair having been gaslit for years. Were it not for the "repeated" and "consistent" requirements under the law, both the husband and wife would be guilty of domestic abuse, which I think many of us would agree would be an absurd outcome).
The second is that - without violence - the victim must be able to demonstrate "serious effect." Without it, there is no offence. A lot of people treat their partner a bit shabbily, but there is nonetheless still a difference between being a shit partner or spouse and being a criminal. The law was designed to protect abuse victims and not so that people exiting messy relationships with sporadic bad behaviours could use the courts for revenge. Unfortunately that means the bar to prove coercive control is very high and possibly too high.
However, regardless, it is not good form to tell someone to believe in the authorities when maybe they will not be very helpful at all. I do agree the OP should report the matter to the police but I would also bet a large sum of money that they won't act on the information.