The UK trade deficit widened to £5.2bn in September from £3.8bn in August, the Office for National Statistics (ONS) said.
Exports decreased by £0.2bn, while imports increased by £1.2bn.
The widening between imports and exports was in part driven by a record £8.7bn deficit with the European Union.
Although the pound fell sharply after the Brexit vote, the ONS said there was little direct evidence so far of currency effects on trade.
After June’s referendum, the pound fell more than 10% against the dollar and the euro, hitting a 31-year low against the dollar, and lost further ground in October to hit its weakest-ever level against a basket of major currencies.
However, ONS statistician Hannah Finselbach said: “So far there is little evidence in the data of the lower pound feeding through into trade volume or prices.”
Between the April-to-June and July-to-September quarters, the total trade deficit for goods and services narrowed by £1.6bn to £11bn.
There was a £4.5bn increase in goods exports and a £3.1bn increase in goods imports between the second and third quarters, partially offset by a £0.1bn decrease in services exports and a £0.3bn decrease in services imports.
Some manufacturers reported a jump in foreign demand after the pound’s fall, but it can take time for this to show up in trade data.
In the three months to September, Britain’s economy slowed much less than most economists had expected, with signs that it was supported by continued robust consumer spending.