Between March and April, prices rose by 1% - the largest monthly rise since June 2014. And the annual pace of growth rose to 5.2%, the first time that this measure has risen in seven months.
The average house price is now £193,048 - the highest figure yet recorded by Nationwide and the first time prices have exceeded £190,000.
"The pick-up in price growth has occurred even though the pace of activity in the housing market has remained fairly subdued in recent months," said Robert Gardner, Nationwide's chief economist.
It follows reports from the High Street banks this week that the number of mortgage approvals is also rising.
The British Bankers' Association (BBA) said approvals were now at their highest level for six months, although still 14% down on their recent peak in March 2014.
In a separate report, housing charity Shelter has claimed that 80% of homes in England are unaffordable for families on average local incomes.
It said that in London, there were only 43 homes for sale that were affordable - and four of them were house-boats.