No.
england-and-wales
People are allowed to film in public, whether it is for publication to YouTube or elsewhere, or not. The classic caveat of sophistry to this used by police to “defuse” situations contrary to the spirit of upholding and informing people of their rights, while rather misleading, but technically true, is that if one puts one’s camera right into someone’s face so as to be overly invasive of their personal space, then this can constitute a section 4A Public Order offence of Intentional Harassment, Alarm or Distress. In practice, this doctrine is really never upheld very far, and is mainly used in the realm of giving “words of advice,” where there is little to no judicial or other scrutiny of the police’s legal theories, and they just get to be annoying and difficult.
Another minor point (effectively of pedantry and moot) is that this isn’t seemingly a public place, but a railway station, accordingly subject to the Railway Bylaws. However, the Railway Bylaws do not proscribe filming others in public if it is done in a civil and reasonable way so as to not breach other bylaws such as against disturbing the peace or comfort of other users of the railways.
But in general, police, however politely or earnestly requested or exhorted by a subject, will never ask someone to stop recording someone else, whether in a public place or on the railway, and will on the contrary firmly uphold the filmer’s largely unconditional right to continue filming.
However, this assumes that the filming is done for personal/household purposes.
data-protection
gdpr european-union
In case, instead, they are done for commercial purposes or otherwise render the filmer into a data controller under the GDPR, then a much more complex and better developed body of law concerning data subject/protection rights comes into play, which balances the above position with various other rights, responsibilities and interests, with the end result in my opinion that the fact still remains that there is no right to stop someone like this from filming you in a public setting.
I’m not familiar with this “pianist and YouTuber” who took the video, and anticipate that some users here who feel less amused and sympathetic toward him, may try to argue that he is indeed a data controller, and perhaps even further that the result of this on the apparent facts is that they do have a right to deny being filmed.
However, I don’t think this would be a matter for the police but rather a civil matter for the courts to grant enforcement of data rights. And I also don’t think that realistically, this regime also has any fangs. The barrier of effort that would be required to even get an order from a court that the rights exist in principle is so impractical as to be prohibitive, but then even having obtained that, the enforcement aspect particularly where the person is an individual rather than an established company would be nearly impossible (if only because of the likely Streisand effect), with the result being that the rights effectively exist only theoretically, if even they do at all.