You won't find anything specific. Legislation doesn't set out to cover every possible situation. However, the Education and Inspections Act 2006 Section 89 gives the head power to regulate the behaviour of pupils. As part of that, it would be permissible for them to ban pupils from leaving the premises without permission other than at lunchtime and the end of the day.
The courts also tend to take a practical approach. If schools had to hand over pupils on demand, a parent could, in theory, avoid a fine for unauthorised absence by simply taking their child out of school after registration for the afternoon, which would defeat the point of attendance legislation. Also, of course, it would be highly disruptive to the school if parents could turn up halfway through a teaching session and demand that their children are handed over.
In the absence of any specific legislation requiring schools to hand over pupils on demand, it is for the courts to decide. They have not yet done so, so we cannot be absolutely certain of the legal position. However, for the reasons given above, I am confident the courts would find that schools are within their rights to limit the circumstances in which a parent can remove a child part way through the morning or afternoon.
Remember that, as far as the law is concerned, the parents have responsibilities, not rights.