Rent in Torridge rose 5% in the past year, new figures show.
It comes as campaign group Generation Rent said renters across Britain are being exploited by an "out of control market" and a lack of protections.
Provisional figures from the Office for National Statistics show the average private rent in Torridge reached £741 per month in the year to September – up 5% from £706 a year prior.
It was also up 27% from an estimated £582 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 £1,139 – rising 6% from the year before.
Torridge had the lowest rental cost in the region, while the highest was in Bristol at £1,753.
Sarah Coles, head of personal finance at Hargreaves Lansdown, said "budget threats" were driving up rents.
She added: "Given the continued exodus of landlords, renters face the double misery of fighting over the scraps and then paying a fortune for them."
In September, the average private rent in Great Britain was £1,295 per month. This was £101, or 8%, higher than 12 months ago.
Meanwhile, separate ONS figures show Consumer Price Index inflation has slowed to 1.7% in September, down from 2.2% in August.
Dan Wilson Craw, deputy chief executive of Generation Rent, said: "Our biggest monthly expense is going up far faster than inflation or our wages."
He added: "Renters are being exploited by an out of control market, and the lack of protections that allow unscrupulous landlords to maximise the rent at every opportunity.
"As a result, renters are unable to save for the future, and many are still making painful decisions about whether to turn the heating on or skip a meal."
He urged the Government to included protections from unaffordable rent rises in the Renters Rights Bill.
"The Government must cap rent increases at the lowest of inflation or wage growth, to stop this huge discrepancy between rent costs and renters’ incomes from widening," he said.
The figures also show the different costs for various homes in Torridge, from £526 for a one-bed property to £1,216 for a home with four or more bedrooms in September.
Among the property types in the area:
- A detached housed cost £986 to rent per month
- A semi-detached cost £809 per month
- A terraced house was £737 per month
- And a flat or maisonette was £599 a month
The Government's Renters' Rights Bill returned to parliament for the second reading earlier this month.
Deputy Prime Minister Angela Rayner said: "I am determined to get this Bill in to law as soon as possible. The thousands of children and families living in unsafe housing or under the cruel threat of a Section 21 eviction notice have been waiting far too long already.
"We will deliver on our promise to renters and transform the sector into one where families can put down roots, where children can grow up in healthy homes, and where young people can save for their future."