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WHEN Charlotte Hobbs decided to teach her 11-year-old pupil about the “imaginary” maths needed to work out the square root of a negative number, she knew it would be a stretch. But her ambition paid off: the girl quickly mastered the concept and now hopes to study maths at university. Most remarkably, Ms Hobbs achieved her feat in a foster home, not a west London Victorian terrace.

Private tuition has long been popular with the rich. A gaggle of London-based firms hire new graduates from Oxford and Cambridge who charge £70-£100 an hour to prepare children for independent-school entrance exams taken at 11 or 13. Yet thanks to ambitious parents and government policies, many more children from lower-income families are being tutored.