document: It said the number of homes on the market was close to record lows, partly because of low rates of construction.
  Nevertheless, its latest figures show that annual house price inflation has fallen, from 5.6% in August to 5.3% in September.
  Between August and September, prices rose by just 0.3%, half the 0.6% rise in the previous month.
  The average price of a house or flat in the UK is now Â£206,015, it said.
  Even though demand for homes has fallen, the number of new properties coming on to the market has also gone down.
  The Nationwide's chief economist, Robert Gardner, said housebuilders should have more confidence that people will want to buy any homes they build.
  And he said they have plenty of sites where they could begin construction.
  "The major housebuilders appear to have capacity to expand output, with most reporting land banks that could support around five years' worth of construction at current rates of building activity."
  Government figures show that in the last year, 139,000 new houses were completed in England. This compares to the need for 225,000 new homes a year, said Mr Gardner.
  "The number of new homes built in England has picked up, but is still not sufficient to keep up with the expected increase in the population," he said.
  The industry responded by saying that there had already been a huge increase in supply, and it was planning to deliver even more.
  "House builders have massively increased output over the past few years and continue to recruit the people and buy the land necessary to deliver even more desperately needed homes," said Stewart Baseley. executive chairman of the Home Builders Federation (HBF).
  "Reversing decades of under supply requires government to continue to implement pro development policies and lenders to ensure buyers can get a mortgage," he told the BBC.
  But Mr Gardner said that in particular, not enough homes are being built in London and its suburbs. Over the last year, the housing stock in the capital has risen by 2.9%, whereas a rise of 4.3% could have been expected, he added.
  Where can I afford to live?
summary: Housebuilders should get on and build more houses, the Nationwide Building Society has declared.