Mrs Keegan said she had been “surprised” to learn that teachers were not required to give advance notice if they were taking part in the strike.
Asked whether teachers should be stripped of their powers to withhold their intention to strike, a Downing Street spokesman said the legal position would remain “under review”.
John O’Connell, the chief executive of the TaxPayers’ Alliance, said: “While teachers have a right to strike, hard-working parents still need to plan their days. Industrial action should come with clear guidelines on how it will impact households.”
Andrew Lewer, a Conservative MP who sits on the education select committee, said: “I think the Secretary of State’s call for teachers to give forewarning before going out on strike is a sensible one, and there is much merit in looking at legislating to this. effect in order to minimize the damage strikes cause to our children’s education.”
The Government risks creating more tension in the battle with the NEU if it pursues a change in legislation.
Kevin Courtney, the union’s joint general secretary of the NEU said: “We already have the most stringent trade union laws in Europe. These laws are designed to reduce the voice of working people at work.
“The NEU along with the TUC [Trades Union Congress] will defend the rights of all workers to be able to exercise their right to strike, without intimidation, in defense of their working conditions and rights.
“Number 10, instead of engaging in these distractions, should be investing in this generation of children and our country’s future.”