The average number of prospective tenants who registered for rental homes per branch rose by 57 per cent from 56 in December to 88 in January.
Year-on-year, demand for rental accommodation has increased by 21 per cent, rising from 73 in January 2019.
However, the number of properties managed per branch fell from 206 in December to 191 in January.
Supply had not been that low since July last year when it stood at 184.
Year-on-year supply was down from 197 in January 2019, but up from 184 in January 2018.
Given the supply and demand imbalance, tenants have seen the cost of renting rise.
More than 40 per cent of letting agents said they had seen landlords increase rents, compared to 32 per cent in December.
Year-on-year, this figure is up from 26 per cent in January 2019, and 19 per cent in January 2018
David Cox, ARLA Propertymark chief executive, said: “This month’s results are a huge blow for tenants. With demand increasing by more than half, but rental supply falling, rent costs are unsurprisingly being pushed up.
“Our recent research found that tenants could miss out on nearly half a million properties as more landlords exit the traditional private rented sector and turn towards short-term lets which will only serve to worsen the problem for those seeking longer term rental accommodation.
“With the Budget around the corner, it’s important the government works to make the private rented sector attractive to landlords again, rather than introducing complex legislation which ultimately squeezes the sector and leaves tenants worse off.”