All teachers in England and Wales yesterday gained the legal right to take half a day off each week for preparation and marking.
Ministers said most schools were ready to ensure their teachers had 10 per cent of their timetable free for planning, preparation and assessment (PPA).
Only 14 schools in England have officially asked the Government for help because of difficulties with the final phase of the national workforce agreement, which became statutory yesterday.
But the National Association of Head Teachers said the real number of schools that would struggle to provide teachers with PPA time was likely to be far higher.
The workforce deal, agreed two years ago, has already freed teachers from carrying out a series of administrative tasks and covering for colleagues for more than 38 hours a year.
Ministers said at least 23,000 of the 23,215 schools, pupil referral units and nurseries in England had reported they were ready to provide PPA time and that 8,000 had started last term.
There was similar optimism from the teachers' unions which supported the agreement.
Chris Keates, general secretary of the NASUWT, said the legal entitlement was a "truly historic development".
She said: "Even in secondary schools where historically teachers had some time away from pupils, it was never guaranteed and was often eroded by requirements to cover for absent colleagues."
But the two main unions that oppose the agreement - the National Union of Teachers and the NAHT - were less positive.
Mick Brookes, the new general secretary of the NAHT, said the association would be investigating how many schools had difficulty providing PPA.
He said: "We think it is regrettable that heads are being put in this position and are having to come up with patched-together solutions to meet the September deadline."
The NUT said it welcomed statutory planning time for teachers, but said that the increased use of teaching assistants could damage the quality of children's education.
The Welsh Assembly said it was not aware of any schools that would have problems providing PPA time, but urged any that experienced difficulties to contact their local authorities.
The Secondary Heads Association has supported the introduction of PPA time as one of the signatories of the workload agreement.
However, John Dunford, its general secretary, writes in today's TES that education ministers should resist loading any more initiatives on to schools as heads would "just say no".