The married teacher missing with his teenage pupil might not have been identified under a new law that comes into force next week.
Teachers will become the first group of people in British legal history to be given automatic anonymity when they are accused of a criminal offence.
The move could hinder searches like the one for missing teacher Jeremy Forrest, who is thought to be in Europe with his 15-year-old student Megan Stammers, critics said.
The provision, in section 13 of the Education Act 2011, gives anonymity for a teacher when the complaint is made by or on behalf of any pupil at the school at which the individual teaches.
The anonymity remains in place until the individual is charged, but can be lifted if an application is made to a magistrates' court.
Bob Satchwell, executive editor of the Society of Editors, condemned the implementation of the provisions as an attack on freedom of speech.
"It will be a criminal offence for anyone - pupil, parent, police, school, local authority, whistle-blower, media - even to inform parents or the general public that an identified teacher has admitted that the allegation is true and has resigned, has been disciplined, or even cautioned for the offence," he said.
"Although we acknowledge teachers' fears about false accusations, the most important issue is surely to protect children.
"Malicious allegations by pupils are extremely rare and, alongside this, the laws of libel, contempt and confidence already restrict newspapers from repeating and publishing unsubstantiated accusations."
He went on: "It is well-meaning legislation where ministers have accepted an argument by teaching unions that some teachers' lives can be seriously damaged by inaccurate accusations.
"But in trying to solve that problem, they're actually causing a bigger problem.
"It's the law of unintended consequences. They're trying to do something which is right, but in doing so they've made the situation worse."
Parents would even be banned from discussing the allegations with their neighbours or other parents with children at the school, Mr Satchwell said.
And the accused teacher could be disciplined, sacked and move on but unless they are charged with a criminal offence, no one could name them and even the new school might not be allowed to know there was a problem, he added.
"People could face prosecution for telling the truth, which seems outrageous," he said.
The fear was that "valid concerns may now be swept under the carpet".
From Monday it will be a criminal offence to publish anything which would identify a teacher who has been accused of assaulting or sexually abusing a child at his or her school if that teacher has not been charged with a criminal offence.
It would even apply if the accusation is referred to in public, for example at an employment tribunal hearing at which the teacher claims unfair dismissal.
The penalty for breaching the anonymity is a fine of up to £5,000.
The Government insisted on pushing the legislation through, but it did make some amendment following intensive lobbying by the Newspaper Society and the Society of Editors.
It argued that anonymity was necessary to protect teachers from the "devastating consequences" of malicious accusations by pupils - even though it was pointed out that only 2% of allegations against teachers turned out to be malicious, and pupils had made only 15 malicious claims in the previous few years.
An application may be made to a magistrates' court for an order to lift the reporting restrictions.
But time could be lost while this takes place and the court may only lift the restriction if it is satisfied that it is in the interests of justice to do so, having regard to the welfare of the teacher concerned and the victim of the offence to which the allegation relates.
No public interest defence has been included in the Bill.
A week after Mr Forrest, 30, and Megan, from Eastbourne, East Sussex, fled together to the Continent, pleas grew for the pair to get in contact.
Mr Forrest's father Jim, of Petts Wood, south east London, fought back tears as he begged his son or the teenager to call or email home.
Flanked by his wife Julie, he said: "Hi Megan, hi Jeremy, I hope this message reaches you and you are both OK. 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.
"We are all here for you both. Please, please get in contact."
As the hunt for the pair intensified, with British officers travelling to France and the issuing of a European Arrest Warrant, there were reports of a possible sighting of the runaways in Paris.
British grandmother Brigitte Ripley, from Bramley, near Guildford, Surrey, told the Sun she saw them walking hand-in-hand and window-shopping in the French capital on Sunday - the day they were due on a ferry back to Britain.
Mrs Ripley, 73, told the newspaper: "I'm as sure as I can be that it was Megan.
"She was in front of me, a youngish girl with long, dark hair. She seemed well, she seemed fine. They were just like anyone else walking around in Paris. They looked like tourists."
Asked why a warrant was not issued until five days after Mr Forrest, who taught maths at Bishop Bell C of E School in Eastbourne, and Megan boarded a ferry from Dover to Calais on Thursday night, Chief Inspector Jason Tingley said their belief was that the pair might use return ferry tickets to come home on Sunday evening.
But Mr Tingley admitted the French authorities have "a slightly different perspective" because what has happened is not seen as an offence in that country, "but we have their full support and we have that team working with us".
Anyone with information is asked to call Sussex Police on 101, quoting Operation Oakwood, or, from abroad, call +44 1273 475 432 or text +44 7786 208 090.
A Department for Education spokesman said: "This change will not affect cases like the one currently getting national attention.
"The police, media organisations and others will be able to apply to a magistrate for an order lifting teacher anonymity.
"If it is in the best interest of the child, this will be granted straightaway so the public can help the police. No teacher who has been charged with an offence, or where a warrant for arrest has been issued, will enjoy anonymity.
"While situations like this are not common, it is the case that malicious and groundless allegations against teachers have been a serious problem in our schools.
"A survey for the Association of Teachers and Lecturers found that one in four school staff has been subject to false allegations from pupils.
"We want teachers to be confident that they can impose discipline without their careers and personal lives potentially being blighted by baseless claims."