The government's "war on red tape" was driven by the 30,000 businesses and individuals that took part in the Red Tape Challenge, which was launched in 2011 to allow the public to highlight pointless and contradictory regulations.
In addition government departments were required to find a double cost saving for any new regulation imposed on business during the current parliament (the one-in, two-out rule).
Hancock said: "One in two out has delivered a fundamental change in the way Whitehall works. We are unashamedly pro-business and we will always back those who create jobs for others.
"Now we are officially winning the fight at home - we have to take the battle against red tape abroad. The EU has committed to reduce the burden of regulations and follow our lead. We need to see action in Brussels to reduce regulation and put jobs and growth first."
Adam Marshall, executive director of Policy and External Affairs at the British Chambers of Commerce, said: "We have long fought for better vetting of EU regulations before they hit the statute book, and will support UK ministers in their efforts to ensure that European regulatory proposals undergo full and proper economic assessments to ensure they don't impose excessive burdens on businesses."
However, BAPC chairman Sidney Bobb said that few of the associations members had noticed any positive difference in business regulation.
"Red tape is of course an uncomfortable challenge with so many businesses in our industry owned and managed by individuals who want to concentrate on getting, producing and despatching work," he said.
"Most owner managers do find administrative tasks somewhat alien to them and the ROI is not particularly obvious. From the conversations I have had with some members it appears that running a business is becoming a more formal exercise and they feel that when one piece of red tape is removed it is not too long before another is introduced."
The government's drive to cut business regulations has led to changes in company law that mean thousands of small businesses now have the freedom to decide whether their accounts need to be audited, saving firms around £300m a year.
The introduction of Early Conciliation in disputes between employers and employees is said to have contributed a further £24m a year in savings by cutting the number of cases that go to Employment Tribunals.
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