House prices rose by 3.9% year on year to October 2015 after a 0.6% monthly rise, Nationwide’s House Price Index shows.
In October prices averaged £196,807, an increase of £1,285 from September.
Robert Gardner, Nationwide's chief economist, said: "UK house prices increased by 0.6% in October, with the annual pace of price growth edging up to 3.9% from 3.8% in September.
"Over the past five months annual price growth has remained broadly consistent with earnings growth over the longer-term.
"While this bodes well for a sustainable increase in housing market activity, much will depend on whether building activity can keep pace with increasing demand."
Jeremy Duncombe, Director of Legal & General Mortgage Club, added: "House prices have continued their steady rise, pushing the dream of homeownership further from reality for many buyers.
"The combination of underwhelming house-building and climbing demand as landlords, first-time buyers and second-steppers compete for their ideal home has caused competition in the market to heat up.
"Not enough houses are coming onto the market and this leads to house prices escalating well beyond the level of inflation, making it difficult for first-time buyers to take that step onto the property ladder and for second steppers to move up.
"The industry and government must work together to rise to this challenge, removing barriers to homeownership and building at least 250,000 new homes every year to alleviate the chronic issue of supply and demand.
"This will ensure more people can achieve their dream of getting the keys to their first home, whilst also giving those at the other end of the market a better opportunity to downsize, freeing up larger houses for growing families."