The UK trade deficit, which reflects the difference between imports and exports, shrank to £4.5bn in July from £5.6bn the previous month, the Office for National Statistics (ONS) said.
The narrowing of the gap reflected a 2% increase in exports of goods and services, taking them to £43.8bn.
Imports fell by 0.5% to £48.3bn.
Although the pound fell sharply after the Brexit vote, which should make UK products cheaper abroad, the ONS said it was too early for firm conclusions.
The pound was 15% lower against other currencies in July compared with the same time a year ago, the ONS said.
The ONS points out in its release that the general consensus among economic commentators is that the recent depreciation in the pound should boost export and manufacturing competitiveness.
However, it says this does not necessarily occur as the price of imported materials used to make UK goods rises as the pound falls.
Analysis: Andy Verity, BBC economics correspondent
Devaluation: the economic equivalent of caffeine. Drop the value of the pound by a tenth and your exporters get a stimulus; suddenly their goods are 10% less in dollars – making them cheaper and therefore more competitive. In the last week and a half, two striking economic updates have been published,suggesting the weak pound has helped.
Today it is the trade deficit. The fact that we as a country buy more than we sell – also known as a trade deficit – has been a persistent problem in the UK for at least two decades. But in July it narrowed by £1.1bn to £4.5bn. The other data was from manufacturers last week, who said the weak pound had helped stimulate the biggest jump in orders and new business for 20 years.
If that effect were sustained then it could help to achieve something the last government only talked about – the re-balancing of the economy. First, away from property and financial services and towards manufacturing and engineering – “making things” (remember the “march of the makers” – the phrase is four years old and empty). And second, away from our chronic dependence on borrowing and financial services to sustain economic growth.
However, be careful. As Matthew Whittaker of the Resolution Foundation pointed out to me on Twitter, finance may be smaller than it was before 2008, but so is manufacturing. And the trade deficit narrowed – but by less than most economists had hoped.
A weak pound may have stimulated the economy, but it has not suddenly improved our underlying economic fitness. Like caffeine, it will eventually wear off.
Howard Archer, chief UK and European economist at IHS Global Insight, said the figures were more evidence of the UK economy’s “current resilience” – despite fears the Brexit vote would stall investment and spending.
He said hopes were pinned on the weakness of the pound encouraging a long-term increase in exports.
“A major hope for the UK economy going forward is that the substantial overall weakening of the pound since the UK voted to leave the European Union in June’s referendum will increasingly feed through to boost foreign demand for UK goods and services,” Mr Archer said.