It said Single Market regulation has been estimated by the House of Commons to cost U.K. businesses around £7.5 billion ($12.2 billion) a year.
By opting out of "several of the more political aspects of the single market created by the EU," they added, the U.K. could save taxpayers money which could then be reinvested in "new U.K. trade missions across the world to promote Britain as a global trading nation and help create jobs."
"We're pushing an idea out there for how we can have this renegotiation," Matthew Elliott, the founder and chief executive of BfB, told CNBC Europe's "Squawk Box."
"I think larger companies are very able to deal with complex, EU regulations but it's the small ones that really get bogged down with it," Elliott added.
"The U.K. Prime Minister's own regulation task force found out last year that lots of businesses aren't being started because of there's too much red tape from the EU."
"What we're saying is, how can you solve this conundrum that [larger] businesses need access to the Single Market to export their goods, but smaller businesses who don't tend to export are really bogged down by the red tape," Elliott added.
"How can we make it [the EU] work for the U.K. to stop us heading for the exit?" Elliott said.
BfB said it was a non-partisan organisation that had reached its conclusions after a six-month consultation program with the business community. Furthermore, it said it had the backing of over 800 of what it calls "leading U.K. business people," along with members of parliament (MPs) and economists.
(Read more: Business optimism boosts hopes of solid UK growth)
Elliott's comments are the latest in a line of high-profile wranglings over the U.K.'s relationship with Europe and tensions over business and trade regulation have increased over the last few years.
Representatives of some U.K. businesses have accused Brussels of introducing bureaucratic and counter-productive legislation that have made doing business in a downturn even harder.
(Read more: UK manufacturing tipped for major turnaround)
In addition, a rise of euroskeptic sentiment among U.K. voters who resent any perceived European interference in economic and political matters has prompted the Prime Minister David Cameron to promise a referendum on EU membership should his Conservative party win 2015 elections.
Unlike more euroskeptic political groups such as the U.K. Independence Party (UKIP) which advocate leaving Europe and its regulatory ties behind for good, BfB's approach appeared to be more of a "one foot in, one foot out" policy favored by mainstream parties.
(Read more: UK CFOs feeling upbeat and ready to take risks)
Prime Minister David Cameron has said the U.K. and the EU need to reform in order to become more competitive, particularly in the face of growing emerging economies and new trade alliances.
- By CNBC's Holly Ellyatt, follow her on Twitter @HollyEllyatt