Rent in Torridge rose 5% over the past year, new figures show.
It comes as Propertymark, a membership organisation for estate agents, said rental supply must rise to meet the increasing demand.
Provisional figures from the Office for National Statistics show the average private rent in Torridge reached £762 per month in the year to April – up 5% from £728 a year prior.
It was also up 28% from an estimated £597 a month five years ago.
Data on rent prices is collected by the Valuation Office Agency from a variety of sources, including landlords and letting agents, with the aim of collecting data on approximately 10% of the market.
Across the South West, the average rent was £1,171 – rising 5% from the year before.
Torridge had the lowest rental cost in the region, while the highest was in Bristol at £1,745.
In April, the average private rent in Great Britain was £1,346 per month. This was £92, or 7%, higher than 12 months ago.
Nathan Emerson, chief executive of Propertymark, said: "Overwhelming demand within the rental sector continues to influence price increases for those who rent."
He added: "We continue to witness, on average, around 10 applicants for every property available to rent and this is a situation that has broadly remained stagnated across the last five years.
"It is imperative that rental supply rises to meet the challenges of demand."
The figures also show the different costs for various homes in Torridge, from £543 for a one-bed property to £1,238 for a home with four or more bedrooms in April.
Among the property types in the area:
- A detached housed cost £1,006 to rent per month
- A semi-detached cost £829 per month
- A terraced house was £759 per month
- And a flat or maisonette was £617 a month