The UK should not prioritise making trade deals around the world at the expense of maintaining close ties with the European Union following Brexit, the government has been warned.

The Institute of Directors, one of the country’s top business lobby groups with more than 30,000 members, said ministers would need to boost trade with both the EU and the rest of the world to make their “global Britain” ambitions a reality.

It comes as Liam Fox, the international trade secretary, looks to strike more trade deals with the rest of the world – seen as one of the key reasons among prominent Brexiters for leaving the EU.

However, polling of almost 800 company directors by the IoD found the EU has provided stronger growth for British firms selling goods overseas than Asia or North America over the past two years.

Business leaders see potential in these regions in the next five years, according to the poll, but the EU remains the area with the highest expectations for growth.

More than two out of five company bosses found most business growth in the EU, compared with one in five citing North America or Asia. Two thirds of those polled exported goods, up by 7% on 2013.

Allie Renison of the IoD warned ministers to “get real about trade, and fast” as the statistics showed how important the EU was for British firms. “Going global is as much about opportunities in Europe as it is further afield, and this should be reflected in how the government shapes post-Brexit Britain,” she said.

A separate study found that three out of four companies are optimistic about their international business prospects. A survey of more than 6,000 firms by HSBC showed mixed feeling about the impact of Brexit, with 38% saying it will be negative, while a third predicted it would be positive.

Amanda Murphy, the head of commercial banking for HSBC UK, said: “Undeterred by future post-EU uncertainty, businesses clearly aim to capitalise on the cheaper pound and rising demand in key markets to boost their overseas sales.”