Richard Donnell, insight director at Hometrack, said: “In the immediate aftermath of the vote to leave the EU there was little obvious impact on the housing market and the rate of house price growth.
"Three months on and it is becoming clearer that households in large regional cities outside southern England continue to feel confident in buying homes and taking advantage of record low mortgage rates where affordability remains attractive for those with equity."
House prices in September grew across all of the cities in the index compared to a year earlier, apart from Aberdeen, where they fell 9.5pc. On a quarterly basis, which compares the three months to September to the three months to June, only Aberdeen and Oxford registered declines.
Property prices in the nation's cities are still growing faster, on average, than other areas of the country. The annual growth rate in the top 20 cities in the index was 8.5pc in September, compared with 7.2pc across the whole of the UK.