Jeremy Forrest, 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.
In CCTV images released of the pair the two are seen holding hands
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.