Called the People's Vote campaign, it is a cross-party initiative supported by pro-EU MPs who want the country to have another referendum before Britain leaves the bloc.
The People's Vote aims to unite anti-Brexit groups, with a rally being held in Camden, north London, on Sunday.
Speaking to the Mail on Sunday, Umunna and Soubry said they wanted to stop a "hard Brexit" - otherwise known as a full, proper Brexit which would free the United Kingdom from the restrictive Customs Union and Single Market that prevent the country from making her own trade deals and controlling immigration.
Both Prime Minister Theresa May's Conservatives and the main opposition Labour Party have ruled out a second referendum after Britons voted 52-48 percent to leave the bloc nearly two years ago, and the country is due to leave the European Union in March next year.
Britain is due to end its membership of the European Union next March, with both the governing Conservatives and main opposition Labour parties rejecting calls for a second referendum. Around 1,200 people attended the event, according to organisers.
The British parliament's only Green MP, Caroline Lucas, said: "This is too big and too important to be determined exclusively by politicians".
"Brexit is not inevitable".
Campaigners including actor Sir Patrick Stewart and politicians from across the political spectrum are demanding a second vote.
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Respondents were asked to what extent they supported or opposed the public voting on the final Brexit deal the British government makes with the EU.
"We are short on time, but we have people power on our side".
"Brexit will affect everybody in the country, which is why it should not be left to 650 politicians to decide our future but 65 million people. If the public demand a People's Vote, politicians will fall in line".
However, foreign secretary Boris Johnson shrugged off the campaign, insisting that the people have already spoken on Brexit.
"They voted with a substantial majority to leave the EU. We're now trying to deliver on that mandate from the people".
The actor, who last January said it was "embarrassed to be British" in a tweet about Brexit, also said he was motivated by "history and emotion" to want to stay in the EU.
"(We) will be able to boldly go again to areas that perhaps we have neglected. friendly wonderful places where we can renew old friendships, rebuild relationships and develop fantastic new free trade deals".