London house prices rose by just 4.2% in the year, the index recorded. This was a lower annual price growth than recorded in 2020.
The rise represented £20,668 increase in the value of a property in the capital in cash terms, and took the average house price of a London home to £507,230.
The index showed "outer Metropolitan" London commuter belt regions recorded steeper average house price rises in 2021.
The category, taking in areas including St Albans, Watford, Maidstone and Reading, saw the average value of a home surge by 8.8% to £410,992.
Average house prices in the "outer South East", which encompasses Brighton and Hove, Oxford, Thanet and Ashford, were up 11.3% to £329,869.
Nationwide's chief economist, Robert Gardner, said: "The price of a typical UK home is now at a record high... Prices are now 16% higher than before the pandemic struck in early 2020."
Gardner pointed to low housing stock on the market being a factor behind "the robust pace of price growth".
The economist warned that the outlook for the housing market in 2022 "remains extremely uncertain”, and pointed out that “housing affordability is already less favourable than before the pandemic struck”.
"It appears likely that the housing market will slow next year,” he said, before adding: “The strength of the market surprised in 2021 and could do so again in the year ahead.
“The market still has significant momentum and shifts in housing preferences as a result of the pandemic could continue to support activity and price growth.”