A survey of wages by Nannytax, a company that provides payroll services for parents and agencies, found that a live-in nanny in London earns £22,582 a year on average — a 12 per cent rise in two years — as well as receiving free accommodation and having bills paid.

Nannytax said that the shortage showed that the era of the live-in nanny was coming to an end.

Asa Nilsdotter, the company’s agency co-ordinator, said: “Just like in any other job where employees do not expect to live with their boss, neither do most nannies.

“It also reflects the changing face of nannying. For a long time it was associated with the super-wealthy and an Upstairs, Downstairs lifestyle where nannies were part of a large staff providing domestic help. Now shift workers in the NHS have nannies, not just highflying City bankers.”

Nanny agencies say that there is strong demand for live-ins, who typically work longer hours and babysit twice a week. Daily nannies now earn an average salary of £28,786, up 6 per cent in two years.

Kate Baker, the founder of Abbeville Nannies in Clapham, South London, said: “When families come to us looking for a live-in nanny, we usually have to tell them we cannot help. Of the nannies on our books, I would say fewer than 1 per cent are now willing to live in, compared with maybe 20 per cent five years ago.

“It’s a real shame, particularly for lone parents or people who work irregular hours and can do with the extra help and baby-sitting.”

Ms Baker said that a change to the holiday working visas for Australians and New Zealanders, who can now work for only one year in Britain, was largely to blame.

“Supply of live-ins has virtually collapsed since the visa change. Australians and New Zealanders were the main source of live-in nannies in London, but families do not want to take someone on for only a year,” she said.

Au pairs were increasingly reluctant to move in with employers, despite the high cost of renting in London, she said.

Working parents pay their nannies’ tax and national insurance contributions, a tradition that dates to the time when nannies were poorly paid.

Two years ago, Gordon Brown introduced a tax break worth up to £2,000 a year to help parents to meet this cost but the survey found that only 3,000 nannies had registered for it, a fraction of the estimated 20,000 workforce.

In order to qualify for the tax break, nannies must register in person at a small number ofdesignated offices during working hours. Those without certain qualifications must then attend two-day courses in childcare and first aid.

Ms Nilsdotter said that the low uptake was disappointinging, but not surprising. “It is a very complicated system with no incentive for nannies to get themselves registered, and the £99 charge doesn’t help,” she said. “I hope that they will change the system so more families take advantage.”

‘It’s a lovely way to work’

Hellen Prideaux, 26, is one of a dying breed of live-in nannies who has no intention of giving up the “huge perks” of sharing a family home (Rosemary Bennett writes).

She looks after four boys aged 4 to 13 for a family in Chiswick, West London, but, with the children now at school, she is moving on to a new live-in position with a family in Chelsea.

At 12 hours, her working day is a long one, but she has benefited from the recent increase in pay for live-ins and earns £340 a week net, with no rent or bills to worry about. “I currently live in a flat owned by the family near their house, which is the best of both worlds. But in my new job I will be living at the top of the house again,” she said.

“It is a lovely way to work. I have no commute, I am here when things happen and the parents can call on me in an emergency. Plus I get to live in a fantastic area I could not possibly afford on my own.”

She said that the nanny and parents must establish clear boundaries. “I take myself off when the parents come home from work because that is their time with the children.”

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