Even a very modest rented home is beyond the reach of low-income households in 33% of of all local authority areas, the Resolution Foundation said.
Private renting is increasingly the only option for millions of families who are not wealthy enough to afford a buyer's deposit or vulnerable enough to qualify for social housing, the foundation said in its report, Home Truths.
The report used the example of a couple with one child and an annual net income of £22,000 to see where they could afford to live if they spent no more than 35% of their net income on housing.
The monthly rent on a modest two-bedroom property ranged from £340 in the cheapest part of the country, Blaenau Gwent in Wales - representing 18% of the family's net income - to £2,380 in the most expensive area, the London borough of Kensington and Chelsea - equivalent to 130% of the same family's net income.
Overall the report found that in 125 of the 376 local authorities in Britain studied (33%), rent would eat up more than 35% of the family's £22,000 net income, making it unaffordable. In 38 of the 376 areas (10%), the rent would consume more than half of their monthly net income.
High rents affect not just London and the South East but create "affordability black spots" across the country, according to the report. Aberdeen, Exeter, South Cambridgeshire and Warwick in the West Midlands are all among the places where private rents are more than 35% of net income for a low-income family, even on a modest property, it said.
Vidhya Alakeson, deputy chief executive of the Resolution Foundation, said: "There is an urgent need to provide more affordable housing for people on low and middle incomes. They are increasingly unlikely to be able to afford the deposit to buy their own home so turn to the private rented sector - but here too they are now struggling to find decent, affordable housing. Incomes for this group are not likely to grow for at least the next five years and this will only make the housing problem more acute."
Housing Minister Mark Prisk attacked the report as "alarmist" and "factually flawed". He said: "It suggests that rents are soaring when in fact they have fallen in real terms. And it fails to recognise that housing benefit provides a safety net which ensures that up to a third of private properties in most areas are affordable to low-income families."