House prices in the UK have broken through their previous peak and the average cost of a home is now higher than ever before, according to the latest monthly survey by the country's largest building society.

Nationwide reported a 13th consecutive month of house prices, bring the cost of an average UK home to £186,512 – more than the previous peak reached in October 2007 before the financial crisis took hold and the overall housing market started to go into freefall.

This is the first time that the index has returned to its peak since the crisis, and news that annual price inflation is now running at 11.1%, its highest level since June 2007, could fuel further calls for policymakers to step in to cool the market.

But at 0.7%, the monthly rate of inflation reported by Nationwide was lower than the 1.2% recorded in April. Also the building society's three-month growth figure, which gives a less volatile picture of the market than month-on-month comparisons, also fell, from 2.5% in April to 2.3% in May. That brought it to the lowest level since August 2013.

The index is based on mortgages approved by Nationwide during the month, and recent lending data has suggested that the introduction of tough new mortgage rules in April led to a slowdown in the market.

Commentators have said it is too early to say if the reduction in activity is temporary or marks the beginning of a cooling off.

Nationwide's chief economist, Robert Gardner, said: "The underlying pace of activity should become more evident as we move through the summer months and the impact of MMR [mortgage market review] 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."

Gardner said first-time buyers were playing an increasingly important role in the housing market recovery. They accounted for 48% of purchases in March – a record high and above the long-run average of 38%.

The government's Help to Buy and Funding for Lending schemes were both designed to assist first-time buyers by making lenders more willing to offer mortgages, particularly to those with small deposits.

Recent figures suggest Help to Buy has been hitting its target, with 80% of borrowing done by new entrants to the market. But in parts of the country where the housing market is growing the quickest the scheme is assisting the smallest percentage of loans.

Nationwide said its analysis showed 4% of mortgages completed in London in the first part of the year were through Help to Buy.

"Low mortgage rates and growing buyer confidence on the back of improving labour market conditions and the brighter economic outlook are probably playing a much greater role in stimulating buyer demand," said Gardner.

The previous high on Nationwide's index was £186,044 which was followed by 16 months of falls, taking the average down to £147,746. The average then started to creep up again, before beginning to take off last summer 2013.

Recently, the chief executive of Nationwide, Graham Beale, said the London housing market could be starting to see a "natural correction" as sales slowed down.

Matthew Pointon, property economist at Capital Economics, said the figures reflected the fact that demand for housing was still outpacing the supply of homes on the market.

"In real terms house prices are still some 20% below the 2007 peak. But we wouldn't take too much comfort from that – after all it is widely accepted that house prices had risen far above any measure of fundamental value during the previous boom," he said.

"With earnings growth very subdued over the past five years, the house price-to-earnings ratio is only around 10% below its previous peak."