House price growth slowed in September, but the recent cooling of demand after the vote for Brexit has largely been offset by a dearth in the supply of homes.

Nationwide said UK house prices grew by 5.3% on average over the year to September, slower than August's annual rate of 5.6%. The average house price was £206,015 ($266,885).

"The relative stability in the rate of house price growth suggests that the softening in housing demand evident in recent months has been broadly matched on the supply side of the market," said Robert Gardner, Nationwide's chief economist.

"Survey data indicates that, while new buyer enquiries have remained fairly subdued, the number of homes on the market has remained close to all-time lows, in part due to low rates of construction activity."

Demand is supported by schemes such as Help to Buy and shared ownership, which make purchasing easier for first-time buyers. And housing supply has been constrained for many years.

Estimates vary, but around 250,000 new homes a year are needed in England to meet demand. Government figures show that there were 142,390 completions in England and Wales in 2015, a 20% annual rise, but well below what is needed.