LONDON (Reuters) - Britain's goods trade deficit was much smaller than expected in May after heavy downward revisions to the previous month's deficit, suggesting some improvement in Britain's trade position was underway before last month's vote to leave the European Union.

Since the referendum, sterling has fallen more than 10 percent on a trade-weighted basis <=GBP> and it hit its lowest against the U.S. dollar <GBP=> since 1985 on Wednesday.

This is likely to lead to the trade deficit widening over the next few months, as the cost of imports surges, but may help it to narrow in the longer term if a cheaper domestic cost base allows British firms to find new markets abroad.

The Office for National Statistics said Britain's deficit in goods alone stood at 9.879 billion pounds versus economists' forecasts of 10.65 billion pounds.

This represented a slight widening from April's reading of a deficit of 9.414 billion pounds, which was 1.1 billion pounds smaller than previously reported.

There was a similar pattern for the overall deficit in goods and services, which stood at 2.263 billion in May, up from a sharply downwardly revised reading of 1.950 billion pounds for April.

British economic growth slowed to a quarterly rate of 0.4 percent in the first three months of 2016, down from 0.7 percent in the last three months of 2015, with Britain's trade deficit accounting for an increased drag.

The ONS did not release figures on trade growth in volume terms, after announcing on Thursday that it needed another week to do further quality checks.

Britain's large current account deficit hit a record 7.2 percent of the economy in late 2015, which the Bank of England has said poses a risk to Britain's financial stability after the vote to leave the European Union in June 23's referendum.

However much of the deficit is due to the weak performance of British overseas investments, rather than its trade deficit.

The ONS also released productivity and unit labor cost data for the first three months of 2016.

This showed quarterly growth in output per hour picked up to 0.5 percent, its fastest since the second quarter of 2015.

But annual growth in unit labor costs - the amount it costs employers to produce a given amount of output - picked up to 1.9 percent from 1.5 percent in late 2015.

Before the referendum some BoE policymakers were concerned weak productivity could cause inflation to accelerate if wage growth picked up. After the 'Out' vote, Governor Mark Carney has expressed fears that any disruption to trade and investment might damage the economy's underlying productive potential.

((Reporting by David Milliken and Andy Bruce))