I was interested to see this issue being covered on the news today, as it is a question I am often asked by parents.
The simple answer is there is no law stating a minimum age, and instead it is for parents to determine when this is safe and reasonable based on the child involved. Leaving a child when it would not be safe, is negligent and can lead to intervention by police and social services.
The NSPCC guidance is helpful, but is only guidance. Legislation on this issue could be useful, but would always be focused on the specific child's individual needs.
BBC Breakfast has found more than 500 people in England and Wales were arrested for leaving their child home alone.