What is the minimum legal requirement on the ratio of adults to pupils for playground supervision?
There is no legal minimum ratio. The ratio of adults to children in the playground is a matter which falls within the duty of care for pupils that every school has. The translation of that duty into practice is the responsibility of the head, who must consider all the relevant factors.
How old are the children? How many of them are there? What is their behaviour pattern and record? What risks are present in this location? What rules are in place to regulate conduct? How competent are the supervising adults? What back-up exists to cope with anemergency?
All these are matters of professional judgment and, although some local education authorities may issue regulations about adult-to-pupil ratios for school journeys and the like, the basic principle is the same.
The best test of any situation is to postulate a "worst case" scenario. Say a pupil is seriously injured while under the school's supervision and the parents sue for negligence. Could the school convince a judge that the level of supervision at the time of the injury was adequate, and what a parent might reasonably be entitled to expect?
The key word is, of course, "reasonably": the school is not required to eliminate all possible risks, even if that were possible.