The last time the annual increase was higher than this was 2010, when the annual change recorded in both April and May was 10.5 percent and 9.8 percent respectively.
Price growth is being supported by supply constraints, as housing completions are still below pre-crisis levels said Nationwide.
(Read more: Bubble alert? UK house prices rise to 6-year record)
"Demand continues to be supported by record low interest rates, improved credit availability and rising consumer confidence thanks to the healthy gains in employment recorded in recent quarters," said Nationwide's chief economist, Robert Gardner in a statement Friday.
The mortgage lender said cash transactions have remained fairly consistent since 2008, as low interest rates in the UK and overseas supported the flow of cash into other assets, including property.
(Read more: Singaporeans continue their love affair with London property)
"These trends may therefore reverse, or at least moderate, in the years ahead if mortgage activity continues to pick up on the back of improving credit availability and labour market conditions," said Gardner.
Cash purchases in London are not out of line with the rest of the U.K., the bank said, despite the greater interest from foreign investors. House prices are in London almost double the level in the rest of the UK -- £345,186 ($577,766) versus £174,444 – in the fourth quarter, Nationwide added.
—By CNBC's Jenny Cosgrave: Follow her on Twitter