The survey of 1,244 employers by Nannytax, which offers nanny payroll service for families, found that parents are prepared to pay up to 65,000 a year for graduates who can speak foreign languages, ski, horse ride and coach children in academic subjects ahead of school entry exams.
Some even wanted skills in dance and karate.
Last year, actress Gwyneth Paltrow too had advertised for a 'supernanny' for her two children, Apple and Moses.
The successful candidate needed to posses a classical education, be fluent in at least three languages, preferably including Mandarin or Japanese, be able to play two instruments, be passionate about sailing and tennis, and enjoy art history or martial arts.
Current vacancies for nannies advertised through Nannies of St James, which recruits for high-profile clients in London, include those for people who can drive, swim but also have a second language.
"For the last three to five years, people have been requesting additional skills, particularly languages. Education is now a priority," the Telegraph quoted Rosemary Newton, partner at Nannies of St James, as saying.
"It's becoming more like America, with parents wanting their children coached for prep school and entrance exams and then wanting nannies to help academically with homework.
"Gone are the days of Mary Poppins. It's become more about the professional, educated, well-rounded graduate," she said.
Successful candidates can reap the rewards of being well qualified, and are often provided with a car and high-quality accommodation on top of a competitive salary.
The survey also found that 68 per cent of families would consider a male nanny, or 'manny' but only two per cent, 23 of those surveyed, have ever actually employed one.
Annie Merrylees, founder and director of My Big Buddy - London's first registered 'manny' agency, specialising in male nannies, said they were popular with single mothers, families with busy fathers, families with only children and ones with disabled children or ones with attention-deficient disorders. She has more than 300 'mannies' in full-time employment.
"Most commonly it's simply families with boys who want someone well-educated who can encourage and assist their children to complete their homework followed by the reward of some active and fun entertainment," she said.