Rent in Torridge rose 5% in the past year, new figures show.
It comes as campaign group Generation Rent said protections must be put in place to prevent rent costs rising above inflation and wage growth.
Provisional figures from the Office for National Statistics show the average private rent in Torridge reached £738 per month in the year to August – up 5% from £702 a year prior.
It was also up 27% from an estimated £580 a month five years ago.
Valuation Office Agency rent officers collect prices from a variety of sources, including landlords and letting agents, with the aim to collect data on approximately 10% of the market.
Across the South West, the average rent was £1,132 – rising 6% from the year before.
Torridge had the lowest rental cost in the region, while the highest was in Bristol at £1,763.
Generation Rent said rent has risen at a faster rate than wage growth across the UK.
Ben Twomey, chief executive, added: "This isn't news to renters, who have been feeling this squeeze for a very long time as our landlords snatch away more and more of our wages.
"The government’s Renters' Rights Bill, published last week, offers many positives for tenants, but the cost of renting crisis will rage on unless Westminster slams the brakes on these runaway rents."
He said the bill must contain protection from unaffordable rent rises and prevent rent rises going above wage growth or inflation.
"Alongside this, we desperately need more homes people can afford to live in, in the places people want to live, and we are pleased that the government have set out this long-term aim."
In August, the average private rent in Great Britain was £1,286 per month. This was £100, or 8%, higher than 12 months ago.
ONS head of housing market indices Aimee North said: "Rental prices continue to climb at a near-record rate, although the pace of the increase has slowed slightly.
"London again saw the fastest growth in rents, with the slowest rise in the south west of England."
Polly Neate, chief executive of Shelter, said: "A severe shortage of genuinely affordable social homes has forced millions of people to rely on the private rented sector, with rents continuing to soar as a result.
She added: "With competition fierce, private renters have no choice but to pay over the odds just to keep a roof over their heads.
"Renters shouldn’t be forced out of their homes by eye-watering rent hikes but over 60,000 have lost their homes to big, unexpected jumps in rent in the past year alone."
She said long term action is needed to tackle rising rents and to provide people with "genuinely affordable" homes, calling on the Government to invest in 90,000 new social homes for ten years.
The figures also show the different costs for various homes in Torridge, from £523 for a one-bed property to £1,213 for a home with four or more bedrooms in August.
Among the property types in the area:
- A detached housed cost £981 to rent per month
- A semi-detached cost £805 per month
- A terraced house was £734 per month
- And a flat or maisonette was £596 a month
A Ministry for Housing, Communities and Local Government spokesperson said: "Our landmark Renters' Rights Bill will introduce extra protections against unreasonable rent increases that stop landlords using large increases to force tenants out."
They added landlords will only be able to raise rents once per year to market rates, and said it will empower tenants to challenge unreasonable increases at a tribunal.
"We’ll also deliver 1.5 million new homes over the next five years, including the biggest increase in social and affordable housing in a generation," they said.