Private rents "eat up" more than 50% of a family's monthly earnings in 23 out of the capital's 33 boroughs.
Shelter said the "rent trap" in the private sector leaves families unable to save towards buying a home and urged London's mayor to intervene.
Mayor Boris Johnson said: "I think it's very important that we expand the supply available."
The report comes after the mayor put out a series of proposals in December to "empower tenants and landlords" in the private rental sector.
Shelter's report, based on an online study by YouGov of 1,397 adults in London in February 2012, found up to half (49%) of the people surveyed said they received "poor or very poor value for money from renting, from letting agents or private landlords".
A third of families also worried about their contract ending before they are able to move out.
Campbell Robb, chief executive of Shelter, said: "The news that renting in the capital is unaffordable isn't a surprise to the families across London who are stuck in the rent trap, unable to save anything towards a home of their own because they are paying out so much each month in rent.
"But the fact that rental costs in most areas of London are eating up more than half of family incomes should stop us in our tracks.
"Rising rents, the constant threat of eviction, and hidden fees are all par for the course in London's frantic rental market."
Mr Johnson said: "I think it's very important that we expand the supply available... we need more on the market altogether.
"What I think is less persuasive is the case for some sort of legislation about renting and prices. The difficulty with that we think is it would tend to drive them (landlords) out of the market."
The mayor's plans include getting funding from the government's Â£200m equity fund for the construction of new homes.
Up to 59% of a typical London family's income is spent on rents, a study by housing charity Shelter has revealed.