LONDON (Reuters) - Britain has long relied on foreigners to fund a big deficit in its balance of payments, a risk that has been heightened by the country's decision to leave the European Union.

Investors have pushed down the value of the pound and demanded higher returns on government bonds because they fear that Britain's economic prospects will diminish.

They are particularly worried by comments from Prime Minister Theresa May who has emphasized that she wants to control migration flows from the EU, something that could limit the country's access to the bloc's single market.

The current account deficit is actually expected to narrow from recent record levels, thanks to the sharp fall in sterling since June's referendum.

But the shortfall, and concerns among investors about it, will probably remain big enough to be a constraint on the government as it prepares for the Brexit process.

Below is an explanation of why Britain has such a big current account problem and what is likely to happen to it.

WHY IS THE DEFICIT SO BIG?

The current account deficit is largely a measure of a country's trade deficit and the difference in money that flows out of the country to foreign investors compared with money flowing in.

To fund the deficit, a country needs to borrow or attract investment from abroad.

The current account deficit hit a record high of 7 percent of gross domestic product in the last three months of 2015. It has fallen back since then, but it is still the biggest among leading rich economies at nearly 6 percent of GDP.

Bank of England Governor Mark Carney said earlier this year that a vote for Brexit could test the "kindness of strangers".

Some of the blame lies with Britain's weak export performance. But the main driver of the deficit in recent years has in fact been Britain's relatively strong economic performance compared with most of its peers.

Higher interest rates on British government bonds and better returns on shares have meant that more money has gone to foreign investors than has come into the country from British investments abroad.

WHAT WILL HAPPEN TO THE DEFICIT?

The good news for the government is that investment outflows look likely to slow after the value of the pound tumbled by nearly 20 percent against the U.S. dollar and almost as much against the euro since the referendum decision in June.

That makes the returns on investment in Britain less attractive to foreigners in currencies other than the pound. It will also boost the value of dividends and bond payments into the country, as measured in sterling.

The weaker pound could help British exporters and make imports more expensive, easing another drag on the deficit.

However, Britain's economy looks set to slow sharply next year meaning the government is likely to sell more debt than it was previously planning. At the same time, households might also rely more on borrowing because an expected rise in inflation in 2017 will hit their spending power.

The International Monetary Fund said this month it expects Britain's current account deficit to narrow from 5.9 percent of GDP in 2016 to 3.8 percent by 2021, which would still be the highest among rich economies.

Economists at Goldman Sachs said on Tuesday that sterling might still be 10 percent too expensive to narrow the current account to more manageable levels.

Similarly, Nomura has said the decline in sterling might only be two thirds of the way to reaching the kind of level that makes British assets attractive again.

WHY DOES IT MATTER?

Sixty years ago, London learned the hard way the vulnerabilities of relying on external financing. The United States used its influence at the IMF - which was considering emergency assistance for Britain - and its own status as a creditor to force London into abandoning a military attempt to seize the Suez Canal from Egypt.

Things are different now, not least because Britain's pound is free to move up or down, giving it a safety valve to cope with changes in the way it manages its economy.

But the current account deficit remains a significant constraint on some of the big decisions facing the government.

Finance minister Philip Hammond will have to tread a fine line on Nov. 23 when he announces Britain's first budget plans since the referendum.

He has said any extra infrastructure spending would be moderate and has shown he is aware that investors might take fright at anything more ambitious, given the still weak state of Britain's public finances.

A recent sharp rise in British government bond yields, albeit from record low levels, has served as a reminder of the power of markets to keep the government on its toes as it prepares to negotiate Britain's future ties with the EU.

"The interplay gets nasty if you start to see a significant section of government bonds being sold," said David Page, senior economist at Axa Investment Managers. "The best way of insuring against that is clarity from the government, which isn't necessarily something we are likely to get."

(Writing by William Schomberg; Editing by Tom Heneghan)