UK goods exports to the European Union fell 40.7% in January, according to the Office for National Statistics (ONS), while imports tumbled.
The figures are the first since the introduction of new trading rules between the UK and the EU.
The ONS said the sharp fall in trade was "likely the result of temporary factors".
Meanwhile, new data showed the UK economy shrank by 2.9% in January as the third lockdown came into force.
The economy is 9% smaller than it was before the start of the coronavirus pandemic.
The ONS said January's fall was a "notable hit", albeit smaller than some had expected.
Retailers, restaurants and hairdressers were all affected by the latest Covid-19 lockdown.