The lender said the annual pace of price growth edged up to 11.1 per cent in May up from 10.9 per cent the previous month.

However, on a monthly basis house prices increased by just 0.7 per cent.

Although this marks the 13th consecutive month of price increases, it represents a slowdown compared to the 1.2 per cent monthly increase in April.

Nationwide said there were “tentative signs” that activity may be starting to moderate following the introduction of tougher lending criteria.

Mortgage approvals in April – the month the tighter affordability rules were introduced – were around 17 per cent below January’s high.

Robert Gardner, Nationwide’s Chief Economist, said: it was “too early to say” whether this was indicative of a cooling trend in the wider market.

“The slowdown may partly be the result of the introduction of Mortgage Market Review (MMR) measures, which may take a few months to bed down,” he said.

“The underlying pace of activity should become more evident as we move through the summer months and the impact of MMR becomes clearer.

“However, with mortgage rates close to all-time lows and labour market conditions continuing to improve, underlying demand for homes is likely to remain strong.”

The report said first-time buyers were playing an “increasingly important role in the housing market”.

They accounted for 48 per cent of house purchase activity in March, a record high well above the long run average of 38 per cent.

However, Gardner said the modest numbers involved so far in the government’s Help to Buy scheme suggests it is unlikely to be the main factor behind the recent pickup in the wider housing market.

Some 12,853 Help to Buy mortgages were completed in the first three months of the year, accounting for around 9 per cent of total mortgage completions over the period.

In London, which has recorded the fastest pace of house growth in recent quarters, Help to Buy accounted for around 4 per cent of mortgage completions in the first quarter, the lowest proportion among the UK regions.

“The evidence suggests that higher priced areas have been seeing the largest percentage increases in house prices, especially in London and the South East, but the majority of Help to Buy loans have been on transactions where the property values are below the national average,” Gardner said.