Research by Barclays found the total value of exports would increase from an estimated £536bn this year to £880bn within a decade.
The United States and Germany would remain the UK's two biggest export destinations, while China would become increasingly important as a trade partner, the report said.
Matt Tuck, head of global transaction banking at Barclays, said: "These latest findings demonstrate the increasing importance of the UK as a global services hub, in addition to the traditional UK stronghold for goods.
"The UK is expected to continue performing strongly with higher-value, higher-margin products in the coming years.
"The outlook for global growth, and UK trade, over the coming years may appear more uncertain than it has been for some time, but as always there will be countries continuing to offer opportunities to UK exporters.
"The transatlantic connection leads the way with the US set to remain our largest individual trade partner over the next 10 years with countries in the EU another key export destination for UK companies."