The success of London schools is at risk as high rents increasingly price young teachers out of London, says the National Union of Teachers.
Teacher recruitment expert Prof John Howson confirmed the rate of teacher vacancies advertised in London was higher than anywhere else in England.
A survey of 1,200 NUT members in London aged under 35 found 60% were planning to leave the city within five years.
And almost two-thirds of these said housing costs were the main reason.
The union has urged candidates in May's mayoral elections to adopt policies to boost affordable housing in London.
Prof Howson, of Oxford Brookes University and director of the Teach Vac website, told the BBC that London schools' teacher recruitment difficulties meant more children were taught by non-specialist teachers, particularly at secondary level.
The NUT says newly qualified teachers in inner London take home £1,655 a month after tax – and £1,583 in outer London.
But the rent on a one-bedroom flat in the capital averaged £1,155 in the year to the end of March 2015, according to government figures.
This compares with £525 for England as a whole and £625 for the south east of England.
This leaves young teachers struggling to make ends meet, says the union.
"Teaching, yes; in London, no. I just can't afford to live here," one teacher told the NUT.
"I can't move further away to find something cheaper as I need to get into work by 07:30," explained another.
Those with families were particularly likely to decide to move.
One teacher said: "I plan to move out because I have a one-year-old and cannot afford to raise my child in London."
Another added: "If I want to have children I would have to change either my city or my profession."
Some cut costs by sharing – but this takes its toll, combined with a teacher's workload, says the union.
"There's no privacy and nowhere to work. Sitting on my bed to mark books is killing my back."
Almost one in five was still living with their parents, blaming escalating rents and stagnating salaries.
"Salaries are little more than they were seven years ago but rent has doubled," said one.
It "makes me feel like I never have my own life. I'm leaving London," said another.
Many called for rent controls, particularly for key workers like teachers.
NUT regional secretary Martin Powell-Davies, said candidates for London Mayor and for the London Assembly must address "this significant and growing problem."
"It they don't, there will be detrimental consequences for London's children and young people's education."
Housing is a key policy area in the race for London Mayor.
Conservative candidate Zac Goldsmith supports government plans to extend right-to-buy to housing association tenants.
If elected, Mr Goldsmith says he will double housebuilding to 50,000 homes a year by 2020 "by working with government to develop London's brownfield land".
Labour's Sadiq Khan says he would focus on building genuinely affordable new homes on public land owned by organisations like Transport for London.
"I'd ensure these new homes are offered to local people first, such as teachers, rather than overseas investors," he says.
Liberal Democrat candidate Caroline Pidgeon says the only way to combat high rents is to increase the housing supply through a City Hall building company.
UKIP's candidate Peter Whittle calls the problem a simple fact of supply-and-demand with "tens of thousands of people arriving in London every year".
For the Green Party, Sian Berry is calling for more new building and a halt to estate demolitions, along with limits to rent rises.