The research, carried out in the manufacturing sector by EEF (Engineering Employers Federation) and funded by RBS, shows exports in the sector have grown by 36% since 2009, with similar growth forecasts for 2012.
But the Forum has warned bank lending must keep pace with the boom if the UK is not to get left behind the rest of the world, and has also said the Government must not cut further resourcing of UKTI (UK Trade and Investment) – the body which helps British businesses break in to foreign markets.
"The Government has made much of the exporting, and this latest research suggests UK manufacturers have certainly been taking notice," said the Forum's Senior Policy Adviser, Phil McCabe.
"But it is now down to the banks to do their bit as well and make sure that firms wanting to export have access to affordable credit to finance such operations. Without the cash to fund these types of operations they can't happen.
"Yet we know from our members' own experiences that banks remain nervous about lending to firms whose business model takes them overseas. It is this risk aversion by the banks that has to end if Britain's economy is to grow on the back of a healthy export market.
"While it's understandable banks would want to closely examine any business plan from a firm looking to trade in foreign markets, it must not be an obligatory ‘no' once they hear the word ‘export' mentioned.
"While exporting does pose new risks for businesses, from customer credit-checking and currency risks to insurances and intellectual property protection, banks themselves need to have a sensible approach to this.
"Banks must accept that while there is increased risk when it comes to exporting, it can dramatically increase turnover and profitability."
The Forum has also said the Government should be wary of further cutting the UKTI budget, especially considering its success despite budget cuts, as more and more businesses look to export. The not-for-profit employer support group says if demand outstrips supply firms could well be put off.
Added Mr McCabe: "While the banks must change their ways, the Government similarly must do its bit by ensuring UKTI has the necessary funding to serve its function properly.
"Today's report suggests UK business is finally ‘getting it' when it comes to the importance of exporting, and the Government now must react accordingly and make sure the support is in place to allow firms to get it right. UKTI does a great job but in order to keep up the good work it needs the right tools for job.
He added: "There hasn't been much good news lately for business, this therefore stands out as something to celebrate. We must not lose the momentum and continue to encourage UK business to fly the flag for Britain on foreign shores."
The Forum of Private Business has welcomed new research suggesting the number of UK firms exporting goods and services has increased, but is urging banks to help keep the momentum going by relaxing lending criteria for firms looking at overseas trade operations.