The following rules apply to the UK, how does the law work here?
. . .concerns about this type of reality TV filming are understandable. Quite apart from the rubbishy television they produce, there is something unsettling about making entertainment out of the police's interaction with the public. There is also the fear that officers might act up for the cameras, or perhaps be more concerned about the state of their hair than about doing their job properly.
But the presence of an independent camera crew filming people in a public place does not alter either the police's duties towards you or your obligations to co-operate with the police. The real issue is what happens to the footage afterwards.
. . .If you object to the presence of a camera crew then there is an argument that "every reasonable effort to minimise embarrassment" should include asking the cameras to be switched off, but the police would not be able to force them to stop filming if they are doing it lawfully – after all there are freedom of expression issues here. If you feel that the police are encouraging or facilitating the filming despite your valid objections then it is arguable that would amount to a breach of the code. This would not give rise to civil or criminal liability on the part of the police, but it might provide grounds for a complaint of misconduct to the Independent Police Complaints Commission.
. . .There are circumstances in which the mere taking of a photograph or video footage will engage the right to private and family life under Article 8 of the European convention on human rights (ECHR) – see, for example, Wood v Metropolitan Police, court of appeal – but in general if the person concerned is in a public place there will be no reasonable expectation of privacy, and any issues under Article 8 will only arise when it comes to the publication of the material.
The publication of footage taken of an identifiable person being questioned, searched or arrested by the police may give rise to a claim against the television company or broadcaster. If the Article 8 rights of the person are engaged this can lead to a claim against a private company through the law of confidence, as the House of Lords confirmed in Campbell v Mirror Group Newspapers.
However, as indicated above, publication will also involve the exercise of the right to freedom of expression under Article 10 ECHR. In these types of cases the courts have to carry out a balancing exercise. One key factor is likely to be whether the person has been convicted of the offence for which he or she was searched or arrested. If there has been a conviction, arguably the right to freedom of expression would outweigh the privacy rights because the conviction will be a matter of public record and the courts will be reluctant to find that privacy rights are engaged by the arrest or apprehension of someone who has committed a criminal offence. If, however, the person has not been convicted because the police did not take any action or there are ongoing criminal proceedings, it would probably be unlawful to publish the footage without the person's consent, whether because of a breach of Article 8 or because it would amount to contempt of court. If the person is not identifiable from the footage, however, no privacy issue will arise in relation to publication.
So in light of all that, probably the best way of dealing with this type of situation is to co-operate with the police but make it clear that this is 15 minutes of fame that you could do without, so the footage should not be published without your consent.