It said the aim was to seek to keep the UK "open for business, open to trade and investment, open to talent and hard work, open to Europe."
Open Britain is described as a cross-party grassroots campaign for Britain to have the "best possible" relationship with Europe in the future now that the country has voted to leave.
This, it states, means working closely on trade, security, workers' rights and environmental protection.
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Three British MPs are the driving force behind the initiative: Anna Soubry, a former Conservative business minister; Pat McFadden, former Labour business minister and Norman Lamb , a former Liberal Democrat health minister.
At the launch on Monday, the three issued a statement, saying, "We will want to shape the debate in Parliament but, more importantly, in the country as well and will be organising campaigning activity in all regions.
"We want to be for the 100 per cent, not just the 48 per cent who voted 'Remain', because while division may have characterised the result on 23 June, we refuse to accept that we have to be a divided country.
"If we interpret the referendum result as a vote for a more insular and less inclusive country, or one in which the only way to advance working people's living standards is to turn our face against the world, we will have converted a defeat into a tragedy. The challenge now is to renew the case for Open Britain."
The launch comes amid a renewed flurry of Brexit-related activity, with UK Prime Minister Theresa May chairing a key meeting of ministers on Wednesday on a "Brexit strategy" while, on the same day, European Council President Donald Tusk meets Belgian Prime Minister Charles Michel in Brussels to discuss the "political and practical consequences" of Brexit.
In Bratislava on 16 September, EU leaders, excluding May, will converge for further discussions on the future of Europe.
Meanwhile, the Socialist group leader in Parliament, Gianni Pittella, has called for a "new pact for Europe", saying a "business as usual" approach to the EU is "impossible" after the EU referendum on 23 June.
The Italian deputy said, "Too much time has been wasted since the vote and we need clarity from the UK government and soon."
He said "cosmetic changes" had to be avoided and the time had come to "move from rhetoric to action."