Theresa May is facing renewed calls from business leaders to ensure the greatest possible access to the European single market after Brexit.
A survey by the Federation of Small Businesses (FSB) found almost a third of its members involved in exporting feared their overseas sales would fall as a result of the decision to leave the EU.
Of the 1,758 members who responded to the survey, 32% were engaged in overseas trade - either as exporters or importers - with the vast majority involved in trade with the single market.
As a result of Brexit, 29% of exporters said they expected a decline in the level of exports - as against 20% who expected to see an increase.
Among importers, 31% said they expected a decrease in their overseas trade compared with 7% who were predicting an increase.
FSB national chairman Mike Cherry said: "Small business exports have been on the rise since the referendum with the lower value of the pound making UK goods and services more competitive.
"As the UK leaves the single market any new agreement must maintain the current ease of trade with the EU and not lead to additional administrative or financial burdens."