Official figures showed exports jumped by 9.1% between March and April, the fastest month-on-month growth since January 2003.
This helped the UK's overall trade gap narrow to £3.3bn in April, the smallest since September, according to the Office for National Statistics (ONS).
It comes after the pound has weakened ahead of this month's EU referendum, making British goods more attractive to overseas buyers.
Sterling hit a three-week low against the US dollar on Monday, falling as much as 0.9% to 1.43 dollars, although it has since bounced back to 1.45 dollars.
Howard Archer, chief UK economist at IHS Global Insight, said that data pointed to "welcome and much-needed" improvements for the economy, BBC reports.
"Along with the jump in industrial production in April and decent retail sales growth, the trade data suggest that UK GDP growth could be holding up better in the second quarter than has been thought, despite the heightened uncertainty," he said.
Sterling fell to its lowest since late 2013 on a trade-weighted basis in April, although falls in the price of UK exports typically take longer to feed through into foreign demand.
However, Mr Archer said that "the marked overall weakening of the pound since late-2015 may be feeding through to help UK exporters".
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