At the same time, the number of landlords putting rents up dropped to the lowest level in seven months, a report from trade body ARLA Propertymark showed.
Almost a quarter of agents reported that landlords increased rents, a steep drop from 31% in September and 40% in August.
Demand from prospective tenants increased in October, but the supply of available properties increased 9% year-on-year to reach its highest level since December 2017.
David Cox, ARLA Propertymark chief executive, said: “Last month’s findings indicate that power in the rental market could be shifting towards tenants, with a record number negotiating rent reductions, and less landlords hiking rent costs.
“However, it’s more likely that this is indicative of the time of year and come the New Year, we’ll see rent prices starting to creep up again.
“There’s no real way of avoiding it unfortunately – with landlords facing continued regulatory change, increasing costs will be passed on to tenants.
“Those who don’t pass the costs on will eventually have to exit the market, which will increase competition and boost prices. It’s the ultimate ‘lose, lose’ situation.”