The TES survey reveals that pupils in 79 per cent of all schools take part in extra-curricular competitive games - the figure for middle schools is 100 per cent and for secondaries it is just 2 per cent lower.
The survey also shows that 78 per cent of schools own their playing field. Again the figures for secondary and middle schools were higher (95 per cent and 94 per cent).
The prime minister is known to have been disappointed when a survey by the Department for Education and Employment revealed that almost half of the nation's schools had not reached his target of a minimum two hours PE a week.
Earlier in the summer Mr Major announced proposals to allow secondary schools to become sports colleges, selecting up to half their intake on sporting ability.
He may now have to come up with something for the primary schools because it clear from the survey they have problems.
Just 74 per cent owned their own playing field and allowed their pupils to take part in extra-curricular competitive games.
Davina Henson, head of Beckington first school in Beckington, Somerset, said: "We have no hall as well as no field and we can only do competitive games with voluntary help in the summer."