"The underlying pace of growth appears to have slowed as a result of weaker global growth and an intensifying of Brexit uncertainty."
Prices saw a modest 0.2% rise month-on-month, after taking account of seasonal factors.
Robert Gardner, Nationwide's chief economist, said: “Average prices rose by around £800 over the last 12 months, a significant slowing compared with recent years – for example, in the same period to October 2016, prices increased by £9,100.
“Indicators of UK economic activity have been fairly volatile in recent quarters, but the underlying pace of growth appears to have slowed as a result of weaker global growth and an intensifying of Brexit uncertainty. To date, the slowdown has centred on business investment, while household spending has been more resilient."
Tiba Raja, director at Market Financial Solutions, commented: "The rate of house price growth is near flatlining, but given the current political and economic environment, this shouldn't be a cause for concern. Buyers and sellers alike are no doubt frustrated by Brexit uncertainty, and many of them are clearly adopting a 'wait and see' approach. And now, with another Brexit delay and a general election on the horizon, it looks as though uncertainty will continue over the coming months.
"Nonetheless, I don't think people have been dissuaded from real estate as an asset class. After all, average house prices have risen since the EU referendum in June 2016 - a positive reminder of UK property's popularity among domestic and international investors."
Karolina Bersadska, client advisor at Nova Financial Group, added: "It is not surprising that Nationwide’s HPI has remained flat this month as it tends to be more South East focused when compared to the Halifax HPI.
"London and the South East is in a stagnant phase which isn’t necessarily due to short term instability as much as it is due to the market having a good upward run over the past five years.
"The North is faring better in the current market but it shouldn’t be viewed as negative when house prices stagnate for a bit as it is a cyclical market that does trend upwards over the mid to long term."
