By Graeme Paton and Martin Evans

Members of the public, the media and even the police could be banned from automatically naming teachers in cases such as that in which Jeremy Forrest fled the country with his pupil, Megan Stammers, it has emerged.

From Monday, anyone who names a staff member at the centre of a criminal allegation made by or on behalf of a child, could face prosecution or a £5,000 fine.

The power, enshrined in the 2011 Education Act, is being introduced to protect innocent teachers against malicious claims from pupils and parents, but critics fear that the legislation has gone too far and will hamper investigations and stifle free speech.

Police chiefs, politicians and senior lawyers specialising in media, have criticised the law, with some warning that it could hamper missing person investigations, such as the one involving Megan.

Douglas Carswell, a senior Conservative back-bench MP, told The Daily Telegraph: “I don’t think this change in the law has been thought through.

“Blanket bans are rarely a good idea and we know about the recent case involving a teacher taking a student to France that sometimes it is right that there is publicity before a warrant is issued.”

Last night when asked about the implications of the change in the law, Graham Stuart, the Conservative chairman of the Commons education select committee, said that the proposals, introduced two years ago under Michael Gove, the Education Secretary, and agreed by the Coalition, could lead to “unforeseen consequences”.

The anonymity law is automatically imposed whenever criminal allegations are made against teachers and would only be lifted when charges are brought or an arrest warrant is issued.

Under the new law the media would have been unable to name Mr Stammers the 30 year-old involved in Megan’s disappearance, until Tuesday when an arrest warrant was formally issued.

Anyone who wishes to force the banning order to be lifted, including the police, will have to make an application to a magistrate, creating what senior detectives believe could be a crucial time delay.

Last night Sussex Police confirmed that the hunt for Mr Forrest and Megan had gone Europe-wide amid fears that the pair could have fled beyond France.

Mr Forrest’s father Jim appealed for his son to let people know Megan was safe. He said: “There are a lot of people back home that are desperate to hear from you. All I am asking is for one of you to make a call, send an email, so we know you are both safe.”

Mr Forrest, who taught maths at Bishop Bell C of E School in Eastbourne, East Sussex, was last seen boarding a Dover-to-Calais ferry with the teenager more than a week ago. Critics warn that the new law could critically delay the identification of individuals in cases in where time is of the essence.

Colin Sutton, a former Detective Chief Inspector with the Metropolitan Police, said: “One of the difficult things with the Megan Stammers case is that they are abroad and it is much harder to get the overseas media involved. If the major tool that you have is the media then this legislation could make things very difficult.”

Niri Shan, head of media law at Taylor Wessing, said: “Unfounded and malicious allegations against teachers are of course extremely damaging, but surely parents also have the right to know what is going on in order to protect their children.”

Santha Rasaiah of the Newspaper Society said: “This is a prime example of the dangers of unnecessary and unjustified restrictions upon freedom of speech. This new offence was created in such wide and ill-defined terms that will obstruct child protection in ways that we have yet to foresee.”

The Department for Education said the law “will not affect cases like the one currently getting national attention” and that magistrates would lift the anonymity order “straight away” following an application from police or the media if children are put at risk. But Mr Stuart added: “What cannot be allowed to happen is for protection of teachers to be put ahead of the protection of children in their charge.”