Paul Smith, chief executive of the Haart agency said: “We believe the nation has now neared the limit in terms of price rises.”

Inquiries dropped in April at the second-highest rate since 2008, according to the Royal Institution of Chartered Surveyors (RICS). Mike Prew, equity analyst at investment bank Jefferies, said: “this slowdown could morph into a period of sustained house price deflation”.

Mortgage approvals nationwide declined by 8.6 per cent in April, far steeper than analysts had expected.

Caution in regard to the EU Referendum is more than likely to have played a role, RICS said.

But broader factors are also at work, such as the slowing economic growth, and not least price rises that have stretched house buyers to breaking point in London and the south east, two places where house price inflation has been most extreme.

Average property prices in the capital rose 54 per cent between the start of 2012 and March this year, according to the Land Registry, contributing to a nationwide rise of 20 per cent. According to Nationwide, house prices in London stand at 9.2 times the average earnings.

Henry Pryor, a buying agent, said he had come across cases where homes remain on the market for three to four weeks and aren’t viewed even once. “How do you persuade people to buy something today that they think will be cheaper tomorrow?” he said.

Lucian Cook, director of residential research at estate agency Savills, said: “We are clearly hitting some affordability ceilings in London.”

Even so, Mr Cook is cynical about the housing market suddenly falling into a drastic downward spiral. If the UK votes to remain a part of the EU “it is difficult to see what the catalyst would be for a significant correction in the housing market”.