Surging house prices and stricter mortgage lending rules are starting to take some of the strongest heat out of the property market as consumers become more cautious, surveyors have reported.

In London, where fears that the market is overheating have been particularly concentrated, demand for properties from prospective buyers slipped back last month for the first time since June 2012, the Royal Institution of Chartered Surveyors (Rics) said.

Surveyors in London have halved their previous predictions for house price growth over the coming years.

They now expect prices to edge up in the English capital by just under 5% a year for the next five years, showing a huge scaling back from a prediction they gave in March that prices would lift at an annual rate of 9%.

This correction would also bring the pace of price increases in London much closer into line with the national average.

While the momentum for property price increases is still "relatively robust", across the country amid a lack of homes to choose from, new buyer inquiries are now rising at the slowest pace seen since February last year.

Surveyors expect UK house prices generally to increase by 3.6% over the next 12 months, marking the most modest prediction seen since last December.

In Scotland, prices are tipped to lift by 2.2% over the next 12 months, while in Wales this figure is predicted to be 3.3% and in Northern Ireland the upswing in values over the next year is expected to sit at around 3%.

Alongside signs that demand is levelling off in the London market, the net balance of surveyors who expect sales to pick up rather than fall in the next three months is also dropping elsewhere, the report said.

For example, an overall balance of 29% of surveyors in the South East expect to see greater market activity in the next few months, down from 66% six months ago, while in the South West this figure has fallen from 93% to 48% over the same period.

Rics said that a continued lack of choice of properties and speculation that the Bank of England was poised to recommend further measures which would apply the brakes more firmly on strong house price increases were factors which were prompting both buyers and sellers to act with more caution.

It highlighted recent figures released by building society Nationwide which showed that UK house prices had reached record levels in cash terms, at £186,512 on average and said its own figures showed that the supply of fresh homes coming onto the market for buyers to choose from had been falling for five months in a row.

A mortgage lending clampdown also came into force at the end of April, which also appeared to be having some impact, the report said.

On average, first-time buyers were perceived by surveyors to need a deposit of nearly 15% in May, compared with a 14% deposit in April.

Under the new Mortgage Market Review (MMR) rules, mortgage applicants have to pass through more detailed checks about their regular outgoings to make sure they can afford their mortgage payments, both now and when interest rates eventually rise.

Simon Rubinsohn, Rics chief economist, said: "What we are really seeing is some of the very strong upward momentum starting to come off the housing market, as a lack of supply, higher prices, more prudent lending measures and some of the talk from the Bank of England are creating a level of caution among sellers and buyers.

"The most visible indicators of this are the revised downwards price expectations for the next 12 months and the flatter picture regarding new buyer enquiries.

"In particular, we're seeing the London market level off."

Mr Rubinsohn said it was hard to tell whether the new MMR rules were just having a temporary influence on the market as lenders adjusted to the changes, or whether there would be a longer-term impact.

There were also signs that more stringent mortgage lending conditions were helping to push up demand again in the rental sector, Rics said.

Looking ahead, rents are projected to grow at around 2.5% over the next 12 months, and at an average annual rate of 4% over the next five years.

Housing Minister Kris Hopkins said: "A key part of our long-term economic plan, and the most important thing we're doing for the housing market, is to get Britain building and increase the supply of new homes.

"Since 2010 we've delivered nearly half a million new homes, including 170,000 new affordable homes, with housebuilding at its highest level since 2007. On top of this, planning permission was granted on 216,000 new homes last year.

"But if buyers can't buy, builders can't build, and leading developers are building more in direct response to our Help to Buy scheme, which to date has helped 27,000 people buy new homes with a fraction of the deposit they would normally require. And our work to tackle the deficit we inherited has helped keep interest rates low and mortgages more affordable, meaning the numbers of first-time buyers are at their highest for seven years."