This piece was originally published on Real Money June 30 at 8:14 a.m. EDT

If there's anything we have learned from the U.K.'s vote to leave the European Union, it is that the unthinkable is much more likely to happen than people expect. One area that investors should watch very closely after the Brexit vote is the U.K. housing market, or more specifically, the London housing market.

The decision announced Thursday morning by South-East Asia's third-largest bank, Singapore-based United Overseas Bank, to suspend loan applications for the purchase of London properties by its customers is a worrying development.

Unlike in the U.S. and in European countries like Spain or Ireland, the U.K. did not see a real house price crash following the financial crisis of 2007-2009. After a dip, house prices took off again, as the Bank of England slashed interest rates and started its quantitative easing program, and the government launched various fiscal-stimulus programs to boost demand for housing.

At the same time, planning restrictions made it very difficult for supply to keep up with increasing demand for housing, while tax relief and cheap lending encouraged retail investors to get into the buy-to-let business -- buying properties to rent them out, with the rent covering the monthly mortgage payments, which usually consisted of paying only the interest on the loan.

These investors, who relied heavily on house prices going up to keep accumulating properties, were the drivers of internal demand for U.K. real estate. In turn, mortgage lending growth heavily depended on them; however, after a last-minute rush to buy before higher stamp duty for second properties came into force in April, they are likely to take a pause.

After last week's vote, consumer confidence plunged to the lowest level since May 2013, when the U.K. economy had begun to emerge from the post-financial crisis slowdown, according to survey data published Thursday. "A recession certainly cannot be ruled out at this point," a representative of the Center for Economics and Business Research, which carried out the survey, said in a statement.

Mohammad Jamei, a senior economist at the Council of Mortgage Lenders, an industry body made of 95% of the mortgage lenders in the U.K., warned that the Brexit vote means activity in the housing market will slow down.

"We expect this to affect sentiment and reduce activity below levels that would otherwise be expected in the near term, as both buyers and sellers adopt a wait-and-see attitude until the dust begins to settle," he said in a statement. But, he added: "Market fundamentals underpinning house prices still look sound, and we do not expect significant house price falls, especially given the current supply-demand imbalance."

If economic activity in the U.K. slows down dramatically, though, internal demand for housing could fall just as dramatically. Many of the immigrants (who are the main victims of last week's vote, as xenophobic and racist attacks jumped more than 50% in the aftermath) could decide to look for friendlier shores and leave the U.K., vacating a few properties, while domestic workers who could be first-time buyers could be affected by job cuts if companies decide to move some operations in the EU.

Foreign demand was supposed to compensate for this, as the weaker pound is making London and U.K. property cheaper for foreign investors. Lauren Awcock, PR Manager at LCP, a specialist residential investment advisery firm focusing on Prime Central London, said in a statement immediately after the vote that foreign investors will still find London property attractive.

"It is predicted that there will be a surge of new buyers, who have been poised on the sidelines awaiting the results," she said, adding that LCP "has already received a stream of enquiries from Asian and Middle Eastern investors" following the Brexit vote.

The government and the central bank have limited methods to further stimulate a housing market where first-time buyers were already stretching the limits of what they could afford to borrow in order to keep up with ever-increasing prices.

Mortgage terms have been extended to 35 or 40 years from the usual 25-year terms, interest rates are at record lows, and the government is already offering equity loans of up to 20% of a property's value outside London and up to 40% in London to help buyers.

It looks like there will be acute need for foreign buyers to flock into London and U.K. property to keep the show on the road. However, the United Overseas Bank's warning could be the harbinger of things to come: "As the aftermath of the U.K. referendum is still unfolding and given the uncertainties, we need to ensure our customers are cautious with their London property investments," it said in a statement.

Investors should pay a lot of attention to this. If the same caution is replicated by other foreign investors, difficult times are ahead for the U.K. housing market and for the economy.