The mortgage lender said that the increase in April was lower than in March, and the trend was likely to continue as budgets were squeezed.
The likelihood of further interest rate rises could also affect the market.
First-time buyers will still be concerned that annual price rises have been in double digits for months.
In all but one month in the past year, annual house price rises have been higher than 10%, the Nationwide said.
Across the UK, it said the average house price in April was £267,620.
The UK housing market is continuing to see demand for properties outstripping the number of homes on the market.
Employment levels have also been relatively steady, despite the pandemic, which has helped to keep demand high, said Robert Gardner, Nationwide’s chief economist. A survey for the building society suggested that 38% of those asked said they were either in the process of moving or considering a move.
This demand has pushed up house prices, despite householders also facing higher food and fuel bills.
Mr Gardner said that the cost of living squeeze would eventually have an impact.
“We continue to expect the housing market to slow in the quarters ahead. The squeeze on household incomes is set to intensify,” he said.
“Moreover, assuming that labour market conditions remain strong, the Bank of England is likely to raise interest rates further, which will also exert a drag on the market if this feeds through to mortgage rates.”