Other cities with strong growth were Leicester (5.3%), Manchester (5.1%) and Glasgow (5.0%).
Liverpool is the highest performing city in terms of house price growth, with an annual rise of 5.7% in March 2019, the Zoopla UK Cities House Price Index found.
Other cities with strong growth were Leicester (5.3%), Manchester (5.1%) and Glasgow (5.0%).
Slowing activity in London, where prices are unchanged year-on-year, seems to be spreading to other areas in Southern England.
Indeed, prices fell by 0.6% annually in Oxford and rose by just 0.7% in Southampton.
Richard Donnell, research and insight director at Zoopla, said: “House prices and sales volumes continue to increase in regional cities outside southern England. Prices in these cities have recorded modest gains over the course of the last decade and affordability remains attractive.
“As employment levels and incomes rise, households have the confidence to bid up the cost of housing, with four cities registering price growth of 5% or more per annum.”
He added: “While sales in London are down 20% on 2015 levels, prices are flat over the last 12 months. The signs of firmer pricing we recorded last month have continued into March with fewer London postcodes registering price falls.
“More realistic pricing and better value for money for potential buyers means sales volumes have stabilised.
“Cities across Southern England are 18-24 months behind London. House prices have increased significantly ahead of earnings in recent years causing the rate of price growth to now slow due to weaker demand and lower sales volumes.
“Price growth is set to remain weak as affordability levels start to re-align with what buyers are prepared to spend.”