Landlords would need to raise rents by £614 a month in London and the South East to remortgage at current rates without making a loss.
Rents would have to increase from £1,498 to £2,112 a month - a jump of 41pc, according to Hamptons estate agents.
Many landlords will sell up as they will be unable to raise rents to such an extent, experts have warned.
The average two-year buy-to-let mortgage rate has reached 6.44pc, while five-year deals are at 6.31pc, according to data company Moneyfacts. Two years ago, the average two-year deal was at 2.96pc.
Chris Norris, of trade body the National Residential Landlords Association, said: "We're seeing lots of people talking about exiting the market at the moment because they're not able to increase the rent - they don't feel it's right or sustainable to increase the rent by the amount they would have to.
"If you're talking about 30 or 40pc, that's not sustainable. The option you're left with is to dispose of that property and to exit."
Half of rental properties sold by landlords are in London and the South East, according to property website Zoopla.
Mr Norris said other landlords are having problems remortgaging when they come to the end of their cheap fixed-rate deals because they can no longer pass stress tests for new mortgage products.
To get a buy-to-let mortgage, basic-rate taxpayers and limited companies need to show that the rental income covers 125pc of the repayment costs.
For higher-rate taxpayers this metric known as an "interest coverage ratio" (ICR) is set at 145pc. Properties with an ICR below 110pc will become unmortgageable and could be moved on to more expensive standard variable rates.
Rents can be increased to meet these standards, but there is a limit to how much more tenants can pay.
In the past year, rents have already surged by 10pc, according to Zoopla. In London and the South East, they have increased by 14pc and 9pc respectively.
Rents have risen faster than pay for 21 consecutive months and now take up 28pc of earnings before tax.
Dan Wilson Craw, of campaign group Generation Rent, said: "We're hitting the limits of what is affordable for tenants."
Rental affordability is at its worst level for a decade in seven of the 12 regions of the UK, according to Zoopla.
Across Britain, 28pc of all landlords face losses if they do not raise rents, accounting for 40pc of landlords with mortgages, according to Hamptons.
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