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 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.
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.